LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

GIRT  OK 

V 
Accession         8t>96$ 


JUNIOR  ARITHMETIC 


A  TEXT  BOOK  FOR  FOURTH  AND 
FIFTH  YEAR  PUPILS 


BY 

CHARLES  E.  WHITE, 

PRINCIPAL  FRANKLIN  SCHOOL,  SYRACUSE,  N.Y. 


BOSTON,  U.S.A. 
D.  C.  HEATH  &  CO.,  PUBLISHERS 


COPYRIGHT,  1895, 
BY  D.  C.  HEATH  &  Co. 


PBESSWOBK  BY  S.  J.  PABKHILL  &  Co. 


TYPOGBAPHY  BY  C.  J.  PETEBS  &  SON,  BOSTON. 


PREFACE. 


In  arranging  the  work  of  this  book,  it  has  been  the 
author's  aim  to  adhere  to  a  proper  order  of  topics,  and 
to  treat  each  topic  with  proper  fulness,  not  only  with 
reference  to  its  business  application,  but  also  with  regard 
to  its  importance  as  a  basis  for  more  advanced  study. 

The  oral,  mental,  written,  and  abstract  work  are  arranged 
in  the  relative  order  and  proportion  that  naturally  lead 
pupils  to  a  clear  understanding  of  processes,  as  well  as  to 
habits  of  rapid  and  accurate  thinking. 

Much  time  may  be  saved  by  early  mastering  the  four 
fundamentals,  particularly  column  addition  and  long  divis- 
ion, frequent  exercises  in  which  occur  throughout  this 
book. 

Pupils  often  attempt  to  solve  problems  before  they  have 
thought  out  the  processes.  This  leads  to  erroneous  re- 
sults, loss  of  time,  and  discouragement.  The  practice  of 
first  indicating  processes  by  means  of  signs  encourages 
the  pupil  to  do  his  thinking  first ;  moreover,  it  often 
permits  a  very  material  shortening  of  the  work  by  can- 
cellation. A  few  pages  of  merely  indicated  work  are  in- 
troduced, to  emphasize  the  advantages  of  such  operations. 

The  latter  can  be  carried  into  the  written  work  of  the 
book  at  the  pleasure  of  the  teacher. 

3 


iv  PREFACE. 

A  few  short  methods,  such  as  multiplying  and  dividing 
by  the  aliquot  parts  of  $1.00,  and  by  the  parts  of  100  and 
1,000,  etc.,  are  introduced.  Pupils  in  the  fifth  year  can 
master  them  readily,  and  at  a  great  saving  of  time. 

Questions  of  relations  (more  fully  explained  in  the  body 
of  the  book)  will  make  plain  a  group  of  difficulties  in 
division  of  fractions  and,  later  on,  prove  of  great  value 
in  percentage  and  its  applications. 

C.   E.   W. 
SYRACUSE,  NEW  YORK, 


CONTENTS. 


CHAPTER  I. 

PAGE. 

NOTATION  AND  NUMERATION 1 

NOTATION  AND  NUMERATION  OF  FEDERAL  MONEY 4 

ADDITION 5 

SUBTRACTION 8 

INDICATED  WORK,  —  ADDITION 11 

INDICATED  WORK,  —  SUBTRACTION 12 

MULTIPLICATION 12 

DIVISION 15 

REVIEW  WORK 20 

INDICATED  WORK, — MULTIPLICATION 21 

FRACTIONS 22 

FEDERAL  MONEY 25 

DRY  MEASURE 26 

LIQUID  MEASURE .  27 

AVOIRDUPOIS  WEIGHT 28 

LINEAR  MEASURE 29 

ADDITION  AND  SUBTRACTION  OF  DENOMINATE  NUMBERS  ....  30 

GENERAL  REVIEW  PROBLEMS 32 

MISCELLANEOUS 44  to  52 

CHAPTER  II. 

FACTORS  AND  MULTIPLES       53 

COMMON  FRACTIONS 66 

LOWEST  TERMS 58 

MIXED  NUMBERS  TO  IMPROPER  FRACTIONS 59 

IMPROPER  FRACTIONS  TO  MIXED  NUMBERS 60 

FRACTIONS  TO  COMMON  DENOMINATOR 62 

ADDITION  OF  FRACTIONS 63 

SUBTRACTION  OF  FRACTIONS 65 

LINEAR  MEASURE 67 

V 


VI  CONTENTS. 

PAGE. 

INDICATED  WORK,  —  DIVISION 68 

INDICATED  WORK,  —  CANCELLATION 83 

DENOMINATE  NUMBERS, — ADDITION  AND  SUBTRACTION    ....  87 

COMPOUND  NUMBERS 105 

GENERAL  REVIEW  PROBLEMS 106 

CHAPTER  III. 

BILLS  AND  ACCOUNTS 117 

ADDITION  AND  SUBTRACTION  OF  FRACTIONS 120 

MULTIPLICATION  OF  FRACTIONS 120 

DIVISION  OF  FRACTIONS 124 

PARTS  OF  A  DOLLAR 128 

THE  THREE  QUESTIONS  OF  RELATION 131 

REVIEW  OF  FRACTIONS 133 

SQUARE  MEASURE 138 

SHORT  MULTIPLICATION 144 

PARTS  OF  100  AND  1000 145 

REVIEW 147 

INDICATED  WORK  AND  PARTS  OF  A  DOLLAR 150 

QUESTIONS  OF  RELATION 156 

MISCELLANEOUS  PROBLEMS 156  to  174 

CHAPTER  IV. 

PLASTERING  AND  PAINTING 175 

CARPETING  ROOMS 177 

PAPERING  WALLS 180 

SHORT  MULTIPLICATION 185 

CUBIC  MEASURE 194. 

CAPACITY  OF  CISTERNS  AND  BINS 197 

MISCELLANEOUS  TABLES 199 

DECIMAL  FRACTIONS 213 

REDUCTION  OF  DECIMALS 218 

ADDITION  OF  DECIMALS 220 

SUBTRACTION  OF  DECIMALS 221 

MULTIPLICATION  OF  DECIMALS 221 

DIVISION  OF  DECIMALS 223 

MISCELLANEOUS  REVIEW 228 


JUNIOR  ARITHMETIC. 


CHAPTER   I. 
NOTATION  AND  NUMERATION. 

A  Unit  is  one,  or  one  thing.     As  1,  1  orange,  f  1. 

A  Number  is  one  or  more  units.     As  1  apple,  10  men,  25. 

The  Unit  of  a  Number  is  one  of  its  units. 

The  unit  of  6  is  1 ;  of  6  pecks  is  1  peck. 

Numbers  having  the  same  unit  are  Like  Numbers.     As  8, 
12,  20,  unit,  1  ;  5  men,  8  men,  12  men,  unit,  1  man. 

A  number  whose  unit  is  1  is  called  an  Abstract  Number. 
As  24,  unit,  1. 

A  number  whose  unit    names  one   particular   thing   is 
called  a  Concrete  Number.     As  24  men,  unit,  1  man. 

An  Integer  is  a  whole  number. 

The  system  of  figures  or  letters  used  in  expressing  num- 
bers is  called  Notation. 

Arabic  Notation  is  used  in  expressing  numbers  by  figures. 
(Illustrate.) 

Roman  Notation  is  used  in  expressing  numbers  by  letters. 
(Illustrate.) 

Numeration  is  naming  the  places  of  figures,  and  reading 
numbers.     (Illustrate.) 

NOTE.  —  Teach  units  of  first,  second,  and  third  orders, 
etc.,  simple  and  local  values  of  a  figure. 

1 


2  ARITHMETIC. 

Three  figures,  standing  in  a  line  from  right  to  left,  form 
a  Group  or  Period. 

Rule. 

Begin  at  the  right  and  separate  the  number  into  groups, 
using  the  comma. 

Begin  at  the  left  and  read  the  number  in  each  group, 
giving  to  it  the  name  of  that  group. 

No  name  is  given  to  the  number  in  the  last  group. 

TABLE. 

3d  Group.  2d  Group.  1st  Group. 

MILLIONS,  THOUSANDS,  ONES. 


1      I 

i  §  § 

III         III         III 

724,  618,  327. 

Seven  hundred  twenty-four  million,  six  hundred  eighteen 
thousand,  three  hundred  twenty-seven. 

Copy  and  read  : 


1. 

2,083 

9. 

713,006 

17. 

72,392,809 

2. 

97,216 

10. 

16,384 

18. 

7,007 

3. 

412 

11. 

219 

19. 

8,100,203 

4. 

88,640 

12. 

9,287 

20. 

21,836 

5. 

9,208 

13. 

291,011  . 

21. 

789,030 

6. 

17,021 

14. 

17,316 

22. 

19,200,036 

7. 

4,903 

15. 

428,063 

23. 

410,004 

8. 

5,007 

16. 

52,913 

24. 

7,200,163 

Write  a  number  containing  three  groups. 


NOTATION.  3 

Write  in  figures  : 

1.  Two  hundred  thousand,  sixteen. 

2.  Eleven  thousand,  two. 

3.  Four  million,  six  hundred  eight  thousand,  three  hun- 
dred seventy-five. 

4.  Twenty-five  thousand,  three  hundred  eighty-seven. 

5.  Nineteen  thousand,  seventeen. 

6.  Twenty-seven  million,  six  hundred  fifty-two. 

7.  Eighty  million,  six  hundred  nine  thousand,  four  hun- 
dred twenty-eight. 

8.  Four  hundred  thirty-six  thousand,  forty-one. 

9.  Six   hundred   twenty   million,   seventeen   thousand, 
four  hundred  seventy-seven. 

10.    One  hundred  fifty-seven  million,  six  hundred  eight 
thousand,  four  hundred  seventy-seven. 

Separate  into  groups  and  read  : 

13087;  716042;  2730010; 

1 26003184 ;  47250627 ;  1002970 ; 

17042;  14390023;  11935079; 

4000030;  29307070;  14280643.  . 

NOTE.  —  Additional  numbers  may  be  dictated. 

Read  these  productions  of  New  York  State  : 
Corn,         17,512,700  bu.  Buckwheat,       4,514,000  bu. 

Wheat,       9,288,000  bu.  Potatoes,          29,688,000  bu. 

Eye,          _  2,724,000  bu.  Tobacco,  6,488,000  Ib. 

Oats,  2,391,000  bu.  Butter,  111,922,423  Ib. 

Barley,        7,418,000  bu.  Cheese,  8,362,950  Ib. 

Hay,  5,426,757  tons.         Hops,  21,628,931  Ib. 

Milk,       231,965,533  gal. 

Write  in  words  the  largest  number  of  two  groups. 


4  ARITHMETIC. 

Read: 

1.  XLV.  6.  MCIV.  11.  DCXCIV. 

2.  CDIL  7.  DCCVI.  12.  MCCV. 

3.  ML  8.  MXIX.  13.  CCXI. 

4.  XIX.  9.  DCX.  14.  MMV. 

5.  LXXXVI.  10.  CDLI.  15.  DLXVI. 
Write  in  Roman  Notation  : 

1.  284  5.      319  9.   2,870 

2.  98  6.    1,515  10.       837 

3.  1,013  7.      745  11.    1,400 

4.  56  8.        47  12.      245 

Notation  of  Federal  Money. 

Federal  Money  is  the  currency  of  the  United  States. 

10  mills  =  1  cent.  Mills  are  not  coined.  The  smallest 
coin  used  is  the  cent.  Cents  are  written  ct.  or  /. 

100  cents  =  1  dollar,  written  $1.  When  dollars  and 
cents  are  written  together,  a  period,  called  the  decimal 
point,  is  placed  between  them.  Thus,  four  dollars  and 
sixty-seven  cents  is  written,  $4.67. 

The  first  two  places  at  the  right  of  the  point  are  occu- 
pied by  cents,  the  third  place  by  mills. 

Nine  cents  four  mills  is  written,  $.094. 

Four  dollars  sixty-five  cents  three  mills  is  written, 
$4.653. 


Copy  and  read  : 

1. 

$  8.40 

2.   $  16.30 

3.  $  92.003 

17.03 

9. 

.105 

2.842 

.087 

256.428 

200.504 

4007.91 

94.02 

Add  the  above.    The  points  must  stand  in  a  vertical  line. 

Write  in  figures  and  add : 

1.    Seventy  dollars  twenty-six  cents. 


FEDERAL  MONEY.  5 

2.  Forty-four  dollars  six  cents  seven  mills. 

3.  Eighty  cents  five  mills. 

4.  Three  thousand  seven  hundred  six  dollars  six  cents 
seven  mills. 

5.  Two  hundred  four  dollars  fifty  cents  three  mills. 

ADDITION. 

Addition  is   the  process    of   uniting   two   or   more   like 
numbers  into  one  sum. 

Add: 


1.  2673 

2.  837 

3.  628 

4.  8063 

846 

2964 

4307 

259 

1025 

418 

526 

8264 

92 

3825 

8279 

1287 

837 

842 

428 

428 

642 

29 

4273 

3064 

5.   $26.43      6.   $715.30        7.   $165.00        8.   $  20.863 


18.75 

21.86 

2.93 

9.246 

4.10 

10.163 

128.06 

7.208 

563.13 

516.00 

28.00 

8.096 

8.429 

129.40 

113.82 

5208.00 

6.804 

.926 

39.625 

128.753 

11.31 

37.15 

476.203 

192.097 

9.  Add  seventeen  thousand,  nine  hundred  six;  four 
thousand,  two  hundred  eighty-nine ;  eight  hundred  twelve 
thousand,  seven  hundred  eight ;  six  hundred  two ;  forty- 
two  thousand,  nine  hundred  two ;  twelve  thousand. 

10.  Find  the  sum  of  eleven  thousand,  six  hundred  seven- 
teen ;  sixty-eight ;  four  thousand,  twenty-five  ;  two  thou- 
sand, three  hundred  nine  ;  eighty-five  thousand. 


6 


ARITHMETIC. 


11.  A    merchant's    sales    were    $2963.84    in    January, 
$1463.27  in  February,  $3846.25  in  March,  and  $2016.92 
in  April.      What  did   his    sales   amount   to   in   the  four 
months  ? 

12.  Find  the  sum  of  all  the  numbers  between  and  in- 
cluding 167  and  174. 

13.  A  man  had  $170  in  his  pocket,  which  was  $70.75 
less  than  he  had  in  his  safe.     How  much  money  had  he  in 
the  safe  ? 

14.  Add  nine  dollars  six  cents ;  fifteen  dollars  seventy- 
two   cents  ;    sixty   dollars   eighty-seven   cents  ;    fifty-nine 
cents ;  four  dollars  five  cents ;  two  hundred  dollars  thirteen 
cents. 


Add: 

15.  4286 
3804 
9273 
6518 
8274 
2936 
8142 
9370 
6425 
3184 
6293 


16.  3184 
2929 
3641 
8207 
9243 
6041 
2938 
8465 
3721 
4936 
8749 


17. 


Add  without  copying : 

18.  178469  19.  729476 

738527  835694 

592946  209731 

846953  569420 

362431  182134 

234234  234123 


2306 
1242 
8936 
6084 
8346 
2920 
1289 
9016 
2914 
8563 
8472 


20.  428756 
937524 
129305 
747925 
165213 
243121 


ADDITION. 

.  "  - 

Add:  Total. 

63  +  59  +  17  +  64  +  23  +  36  = 
87  +  84  +  68  +  82  +  72  +  28  = 
42  +  35  +  49  +  39  +  18  +  65  = 
96  +  42  +  28  +  50  +  25  +  32  = 
54  +  96  +  16  +  26  +  16  +  44  = 
83  +  73  +  94  +  45  +  25  +  46  = 
28  +  18  +  31  +  13  +  23  +  32  = 

Total, 

Oral  Work. 

1.  Ruth  had  17  cents,  and  earned  8  cents  more.     How 
many  cents  had  she  then  ? 

2.  40  +  12  +  10  =  ? 

3.  We  had  62  books  in  our  library  and  bought  18  more. 
How  many  have  we  now  ? 

4.  Five  pupils  are  absent  from  a  class  and  38  are  pres- 
ent.    How  many  pupils  are  there  in  the  class  ? 

5.  Edward  had  29  cents  in  his  bank  and  put  in  6  more. 
How  much  money  has  he  now  ? 

6.  There  are  42  pears  in  one  box  and  39  in  another. 
How  many  in  both  boxes  ? 

7.  Albert  spent  8  cents  for  a  ball,  4  cents  for  a  pencil, 
and  12  cents  for  a  writing-book.     How  much  did  he  pay 
for  all  ? 

8.  Willard  had  28  marbles  in  one  bag  and  12  in  another. 
How  many  had  he  in  both  bags  ? 

9.  A  boy  sold  a  pair  of  skates  for  $.75,  which  was  $.25 
less  than  they  cost.     What  did  they  cost  ? 

Add  quickly  : 

16        19        24        14        32        29        17 
9          8          7        12          8        11        18 


8  ARITHMETIC. 

SUBTRACTION. 

Subtraction  is  the  process  of  finding  the  difference  be- 
tween two  like  numbers. 

The  Minuend  is  the  number  from  which  we  subtract. 
The  Subtrahend  is  the  number  subtracted. 

The  result  in  subtraction  is  called  the  Difference  or 
Remainder. 

How  can  you  find  the  minuend  when  the  subtrahend  and 
remainder  are  given  ?  (Illustrate.) 

How  can  you  find  the  subtrahend  when  the  minuend 
and  difference  are  given  ?  (Illustrate.) 

1.        2819      2.          8203       3.          4295      4.          7306 

-  674  -1276  597  -1807 

5.        2763      6.        37284       7.        36801      8.        18003 

—  1289  -    9287  -  18463  921 

9.    From  seventeen  thousand  sixteen,  take   nine  thou- 
sand four  hundred  eighty-seven. 

10.  From  seventy-two  thousand  three  hundred  eleven, 
take  forty-six  thousand  nine  hundred  sixty-one. 

11.  Take  eight  thousand  four,  from  thirty  thousand. 

12.  Find  the  difference  between  sixteen  thousand  four 
hundred  seventy-five,  and  twenty  thousand  seven  hundred 
twenty-seven. 

Subtract : 

1.   92874   2.  -  8206   3.  -38706   4.  -26942 

-  11392       94210       42840       98301 

5.   38264   6.  -  8291   7.    92593   8.   27075 

—  29842       19327     —  87246     — 18092 


SUBTRACTION.  9 

1.  The  minuend  is  7026  and  the  subtrahend  987.    Find 
the  difference. 

2.  Find  the  difference  between  9284  and  13411. 

3.  $4216.56  -  $1874.92  =? 

4.  $149.725  -  $69.417  =? 

5.  Take    sixteen   thousand   eight    hundred   seventeen, 
from  twenty-four  thousand  five  hundred  forty-one. 

6.  The    difference    is   8037.     The   minuend   is    19406. 
Find  the  subtrahend. 

7.  Take  seventy-six  dollars  four  cents  two  mills,  from 
one  hundred  two  dollars  nine  mills. 

8.  From  sixty-five  thousand  three  hundred  sixteen,  take 
twenty-four  thousand  forty. 

9.  Take  $86.215  from  $900.09. 

10.  What  must  be  added  to  $.67  to  make  $3  ? 

11.  From  a  farm  of  263  acres  of  land  97  acres  were  sold. 
How  much  was  left  ? 

12.  A  man  had  $279,  and  spent  $129.64.     How  much 
had  he  left  ? 

Oral  Work. 

1.  If  8  apples  are  taken  from  a  basket  containing  25, 
how  many  apples  are  left  ? 

2.  James  is  7  years  younger  than  his  brother,  who  is 
21  years  old.     How  old  is  James  ? 

3.  If  you  have  $1.25  and  spend  $.75,  how  much  have 
you  left  ? 

4.  A  farmer  sold  a  horse  for  $125.     If   it   cost   him 
$140,  how  much  did  he  lose  ? 

5.  How  much  more  than  32  is  45  ? 

6.  Fred  has  32  marbles  and  Robert  has  18.    How  many 
more  has  Fred  than  Robert  ? 


10 


ARITHMETIC. 


7.  Find  the  difference  between  36  and  45. 

8.  If  you  give  a  fifty-cent  piece  in  payment  for  a  book 
which  cost  35  cents,  how  much  change  should  you  receive  ? 

Subtract : 

29  30  25  48  35  GO 

-12          -16  -13          .-15 


ADDITION  AND  SUBTRACTION. 

Add,  without  copying : 


1.   417 

2.   1172 

3.   1642 

4.   183 

28 

2964 

417 

2057 

135 

42 

305 

125 

2906 

4281 

2893 

748 

Subtract, 

without  copying 

s 

5.  1187 

6.  -  1375 

7.  -2156 

8.  7073 

-242 

9100 

4228 

—  496 

Add: 

9.  2786 

10.   5278 

11.  43562 

12.  22879 

1947 

4492 

84601 

43012 

1838 

8913 

92873 

92874 

5287 

6472 

26461 

69154 

6496 

7258 

30725 

82738 

8035 

5603 

92837 

56425 

2956 

8450 

68154 

78997 

8375 

7921 

15210 

37684 

1698 

2864 

2835 

1872  • 

3263 

1342 

5832 

5832 

Subtract  : 

13.  10392 

14.  -28023 

15.   7296 

16.  __  73841 

-3875 

38641 

-629 

92040 

INDICATED    WOliK.  11 

Oral  Work. 

1.  A  man  travelled  36  miles  one  day  and  13  the  next. 
How  many  miles  did  he  go  in  both  days  ? 

2.  Edith  wrote  28  words  in  the  morning  and  17  in  the 
afternoon.     How  many  words  did  she  write  ? 

3.  John  used  17  sheets  of  paper  from  a  tablet  containing 
65  sheets.     How  many  are  left  ? 

4.  James  had  22  cents  and  earned  3  more.      He  spent 
18  cents  for  a  knife.     How  much  had  he  left  ? 

5.  What  must  be  added  to  16  +  12  to  make  30  ? 

6.  Two  trains  leave   Syracuse,  and  move  in  opposite 
directions.     One  goes  42  miles  and  the  other  34.     How  far 
apart  are  they  ? 

7.  Anna  had  $  1.     She  spent  $.42  for  a  book  and  $.08 
for  a  tablet.     How  much  had  she  left  ? 

8.  Two  boys  skate  in  the  same  direction.     One  goes  57 
yards  and  the  other  49  yards.     How  far  apart  are  they  ? 

Indicated  Work.  —  Addition. 

NOTE.  —  Pupils  should  be  taught  to  indicate  the  opera- 
tion before  finding  result. 

Indicate  the  addition,  by  using  sign,  and  give  the  result. 

1.  4  and  5.  4.    5,  17,  26,  and  39. 

2.  36  and  45.  5.    16,  15,  18,  and  26. 

3.  36,  15,  16,  and  38.  6.    29,  84,  72,  and  56. 

7.  A  lady  found  3  roses  on  one  bush,  5  on  another,  and 
.7  on  another.     How  many  roses  did  she  find  ? 

8.  James  found  2  eggs  in  a  hen's  nest,  5  in  another,  and 
6  in  another.     How  many  eggs  did  he  find  in  all  ? 

9.  The  sum  of  25  cents,  38  cents,  and  18  cents. 

10.    The  sum  of  16,  18,  and  56,  added  to  the  sum  of  25, 
19,  and  34. 


12  ARITHMETIC. 

Indicated  Work.  —  Subtraction. 

Indicate  the  subtraction  and  give  the  result. 

1.  29  from  84.  3.    $.74  from  $1. 

2.  63  minus  42.  4.    $8.35  from  $9.14. 

5.  Nineteen  books  are  taken  from  a  case  containing  130 
books.     How  many  are  left  ? 

6.  A  man  spent  $10.16  on  Monday  and  $4.40  on  Tues- 
day.    How  much  more  did  he  spend  on  Monday  than  on 
Tuesday  ? 

7.  A  boy  had  36  marbles.    He  lost  5  one  day  and  11  the 
next.     How  many  had  he  left  ? 

36  _  (6  +  11)  =  ? 

8.  If  you  have  60  cents  and  spend  18  cents  for  ribbon 
and  12  cents  for  thread,  how  much  have  you  left  ? 

MULTIPLICA  TION. 

Multiplication  is  a  short  method  of  adding  equal  numbers. 
Add  four  5's. 

ADDITION.  MULTIPLICATION. 

5  5  multiplicand. 

5  _4  multiplier. 

5  20  product. 

_5 
20 

The  Multiplicand  is  one  of  the  equal  numbers  added. 
The  Multiplier  is  the  number  of  equal  numbers  added.    • 
The  result  of  multiplication  is  called  the  Product. 
The  multiplier  is  never  a  concrete  number. 
The  multiplicand  and  product  are  like  numbers. 
The  product  is  the  same  in  whatever  order  the  numbers 
are  multiplied.     (Illustrate.) 


MULTIPLICATION.  13 

NOTE.  —  Teach  how  to  multiply  by  10,  100,  1000. 

Multiply : 

1.  36  X    10        4.       28  X    100        7.     100  X      10 

2.  100  X    16         5.      328  X  1000         8.      100  X    100 

3.  236  X  100        6.   1000  X    512        9.    1000  X  1000 
Multiply : 

1.   872        2.   943        3.     206        4.   985        5.   876 
16  24  37  59  84 

6.   467        7.   317        8.    2936        9.    416       10.   487 
238  504  28  834  236 

Oral  Work. 

1.  536  X    10  6.     289  X    100 

2.  10  X  694  7.    1000  X      36 

3.  786  X    10  8.   1000  X    586 

4.  '  100  X  395  9.     369  X    100 

5.  1864  X  100  10.     289  X  1000 

283  X  300  ==  ?     Annex  two  naughts  and  multiply  by  3. 
Write  answers  only : 


1. 

286 

X 

20 

6. 

384 

X 

2000 

2. 

25 

X 

20 

7. 

5000 

X 

382 

3. 

400 

X 

253 

8. 

9000 

X 

35 

4. 

500 

X 

286 

9. 

2811 

X 

10 

5. 

29 

X 

900 

10. 

27 

X 

700 

Multiplication. 

1. 

2087 

X 

42 

5. 

746 

X 

835 

2. 

186 

X 

294 

6. 

3006 

X 

48 

3. 

1238 

X 

400 

7. 

1283 

X 

680 

4. 

653 

X 

29 

8. 

967 

X 

105 

14  ARITHMETIC. 

1.  If  there  are  196  pounds  in  a  barrel  of  flour,  how 
many  pounds  in  240  barrels  ? 

2.  Find  the  product,  the  multiplicand  being  three  thou- 
sand five  hundred  seventy-eight  and  the  multiplier  four 
hundred  six. 

3.  How  many  bushels  of  apples  will  4  orchards  produce, 
if  there  are  84  trees  in  an  orchard,  and  the  average  yield 
10  bushels  to  a  tree  ? 

4.  $126.34  X  28  =  ? 

5.  Fifteen  men  earn  $1.25  each  in  a  day.     What  will 
their  combined  wages  amount  to  in  a  week  ? 

6.  Multiply  six  hundred  nine  by  forty-eight. 

7.  $720.036  X  14  =  ? 

8.  Seventy-four  yards  of  carpet  at  $1.08  a  yard,  will 
cost  what  ? 

9.  Multiply  nine  dollars  six  cents  two  mills,  by  17. 

10.    Find  the  cost  of  472  bushels  of  apples  at  $1.20  a 
bushel. 

Oral  Work. 

1.  How  many  pens  in  2  boxes,  if  there  are  144  pens  in 
a  box? 

2.  How   many   dimes  in  27  dollars,   if   there  are   10 
dimes  in  a  dollar  ? 

3.  How  many  trees  in  6  rows,  if  there  are  15  trees  in 
a  row  ? 

4.  How  many  quarters    in   42    dollars,  there    being  4 
quarters  in  a  dollar  ? 

5.  How  many  pounds  in  3  sacks  of  flour,  if  there  are 
49  pounds  in  a  sack  ? 

6.  How  many  desks  in  three  schoolrooms,  there  being 
9  rows  in  each  room  and  7  desks  in  a  row  ? 


DIVISION.  15 

DIVISION. 

Division  is  the  process  of  finding  how  many  times  one 
number  is  contained  in  another. 

The  number  divided  is  the  Dividend. 

The  number  by  which  the  dividend  is  divided  is  the 
Divisor. 

The  result  of  division  is  called  the  Quotient. 

When  the  divisor  is  not  exactly  contained  in  the  divi- 
dend, the  part  of  the  dividend  that  is  left  is  called  the 
Remainder.  (Illustrate.) 

The  remainder  and  dividend  are  always  like  numbers. 
(Illustrate.) 

When  the  divisor  is  an  abstract  number,  the  dividend 
and  quotient  are  like  numbers.  (Illustrate.) 

When  the  dividend  and  divisor  are  concrete,  the  quotient 
is  abstract.  (Illustrate.) 

The  sign  of  division  is  -5-,  and,  when  placed  between  two 
numbers,  signifies  that  the  first  is  to  be  divided  by  the 
second.  As  12  ~-  3  =  4. 

Division  is  also  indicated  by  writing  the  dividend  above, 
and  the  divisor  below,  a  dividing  line.     Thus,  ^  =  4. 
Find  the  quotients  : 

1.  18^6  3.    if  5.    63-7-9  7.    ^ 

2.  14 -T- 2          4.   \&          6.   28 -T- 2          8.   3^ 
Find  the  quotients  at  sight : 


1.      5  in    15 
2.      8  in    32 
3.      9  in    72 
4.    11  in    99 
5.    12  in  132 

6.      5  in    60 
7.    11  in    88 
8.    10  in  100 
9.    11  in    77 
10.    12  in    84 

11.      75  -i-    5 
12.      56-5-8 
13.      21--7 
14.      63  ^-    7 

15.      96  -4-  12 

16  ARITHMETIC. 

SHORT  DIVISION. 

6)1974  Six  is  not  contained  in  1  (thousand),  hence 
329  we  find  how  many  times  6  is  contained  in  19 
(hundreds),  which  is  3  (hundreds)  times,  with  a  remainder 
of  1  (hundred).  Write  the  3  hundreds  under  the  hundreds 
of  the  dividend.  Change  the  remainder  1  (hundred)  to  tens, 
and  add  it  to  the  seven  (tens),  making  17  (tens).  Dividing 
this  by  6,  we  have  2  (tens)  for  a  quotient,  which  is  placed 
under  the  tens  in  the  dividend,  and  5  (tens)  for  a  remain- 
der. Changing  this  remainder  to  ones,  and  adding  the  4 
(ones),  we  have  54  (ones),  which,  divided  by  6,  gives  9 
(ones),  which  is  placed  under  the  ones  in  the  dividend. 
The  quotient  is  329. 

Prove  by  multiplying  the  quotient  by  the  'divisor  ;  if  it 
equals  the  dividend,  the  work  is  right. 

Divide  by  short  division  : 

1.  2555-4-5  10.  ^jpjL  19.  30005—   5 

2.  2436-4-4  11.  **f^  20.  288012  —  12 

3.  2845  -r-  5  12.  *af*a.  21.  300010  —  10 

4.  4503-7-3  13.  lajia  22.  99011-11 

5.  2045  -r-  5  14.  AAJAA  23.  33264-11 

6.  2835-7-7  15.  J-LflAi  24.  29280  —  12 

7.  4986-4-9  16.  lifaa  25.  36550  —  10 

8.  2009-7-7  17.  S^AJL  26.  28692—    9 

9.  3504  -T-  8  18.  S-&J4JL  27.  333333-4-11 


8)3989  After  dividing,  there  is  a  remainder  of   5, 

498  f     which  must  be  divided  by  8.     This  we  can 
X  8       oniy  indicate  thus,  £.     The  quotient  is  498|. 

To  prove,  multiply  the  integral  part  of  the 
*"          quotient  by  the  divisor,  and  add  the  remainder. 

QQQQ 

If  it  equals  the  dividend,  the  work  is  right. 


LONG  DIVISION.  it 

Divide : 

1.  35621-4-7  3.   31493^6          5.   82956 -r- 10 

2.  42963-5-6  4.   50725-4-3          6.   93043-4-    7 
To  divide  by  10,  100,  or  1000. 

1|QO)369|00  1|00)283|25  1|000)36|954 

369  283^  36TVo4o 

Cut  off  from  the  right  of  the  dividend  as  many  figures  as 
there  are  naughts  upon  the  right  of  the  divisor. 

1.  39826-4-    100    5.   26935 -j-    100    9.     39482-4-1000 

2.  28964  -f-  1000     6.   26320  -4-      10  10.       2896  -4- 1000 

3.  389000  -4- 1000     7.    61934  --  1000  11.      99208  -4-    100 

4.  42657  -4-      10    8.   40030  -4-    100  12.    500300  -4-      10 

LONG  DIVISION. 
Divide  1234  by  15. 

82^     Quotient. 

15)1234  SOLUTION.  — 15  is  not   contained   in   12 

(hundreds),   so  we  must  include   the   tens. 
15  is  contained  in  123  (tens)  8  (tens)  times. 
Multiplying  8  (tens)  by  the  divisor,  we  have 
120  (tens),  and  subtracting  we  have  3  (tens), 
which,  changed  to  ones  and  added  to  the 
4  (ones)  makes  34  (ones).     15  is  contained  in  34  (ones), 
2  (ones)  times.     Multiplying  2  (ones)  by  the  divisor,  we 
have  30  (ones),  which,  subtracted  from  34  (ones),  leaves 
a  remainder  of  4  (ones).     4  (ones)  divided  by  15  is  -^, 
which  is  placed  as  part  of  the  quotient.     The  entire  quo- 
tient is  82yV 

Divide  : 

1.  14)392  2.  17)485  3.  16)507  4.  13)296 

5.  18)1124  6.  15)793  7.  22)943  8.  19)1364 
9.  24)3726  10.  27)851  11.  21)1240  12.  32)3964 


18  ARITHMETIC. 

13.  1289 -r- 16  27.  5630-^-62 

14.  5683 -r- 37  28.  1289-^-73 

15.  5436 -;- 18  29.  16428-7-84 

16.  1286 -r- 39  30.  12582 -,-58 

17.  2983-42  31.  1384-^-75 

18.  1008-^-25  32.  6381 -r- 86 

19.  9436-47  33.  12946 -T- 24 

20.  8059-^-36  34.  9273 -r- 91 

21.  1583  -v-  46  35.  7754 -f- 78 

22.  4109-^51  36.  10846 -T- 45 

23.  2695 -;- 57  37.  21431-^36 

24.  3874^49  38.  27473 -T- 97 

25.  9003 -T- 25  39.  35702 -f- 53 

26.  5914 -T- 59  40.  40060 -f- 60 

41.  Divide   seven   thousand,  four  hundred   sixteen,   by 
twenty-seven. 

42.  A  ship  sailed  159  miles  in  13  days.     How  far  did  it- 
sail  in  one  day. 

43.  $96.64.  was  divided  equally  among  16  men.     How 
much  did  each  receive  ? 

44.  How  many  pounds  of  butter  at  $.18  a  pound  can 
be  bought  for  $8.82  ? 

45.  How  many  times  is  19  contained  in  4845. 

46.  Divide  $137.34  by  18. 

47.  Divide  $62.826  by  74. 

48.  A  farmer  wishes  to  put  9216  bushels  of  oats  into 
bins  holding  16  bushels  each.    How  many  bins  can  he  fill  ? 

49.  Divide  six  thousand,  seven  hundred  and  sixty-seven 
dollars,  thirty-nine  cents,  seven  mills,  by  sixty-seven. 


INDICATED   WOKK.  19 

Oral  Work. 

1.  At   $.12   each,  how  many  books  can  be  bought  for 
$.72? 

2.  Divide  $1  equally  among  5  boys. 

3.  How  many  dozen  are  84  oranges  ? 

4.  When  8  pounds  of  butter  cost  $2,  how  much  is  it  a 
pound  ? 

5.  Four  boys  together  earned  $4.16.     What  should  each 
receive  if  they  all  earned  the  same  amount  ? 

6   56  -r-  14  =  ?  60  -r- 15  =  ?  75  -^  25  =  ? 

7.  A  class  of  25  scholars  wrote  250  words.     How  many 
words  did  each  scholar  write  ? 

8.  Among  how  many  men  can  $45  be  divided,  if  each 
man  receives  $15  ? 

9.  There  are  108   pencils  in  9  packages.     How  many 
pencils  in  a  package  ? 

Indicated  Work. 

1.  James  had  18  marbles  and  found  5  more.     He  after- 
wards lost  8  marbles.     How  many  were  left  ? 

2.  A  boy  deposited  $1  in  the  savings-bank  on  the  1st  of 
the  month,  75/  on  the  10th,  and  $2.50  on  the  25th.     On 
the  30th  he  drew  out  $2.75.     How  much  was  left  in  the 
bank? 

3.  John  had  $5.18  in  the  bank.     He  drew  out  $1.50  on 
Monday,  and  $.75  on  Tuesday.     How  much  had  he  left  ? 

$5.18  —  ($1.50  +  $.75)  =  ?     Teach  use  of  parentheses. 

4.  The  sum  of  5  and  9  taken  from  16.     (Problem.) 

5.  The  sum  of  56  and  39  taken  from  188.     (Problem.) 

6.  The  sum  of  36,  15,  and  87  taken  from  the  sum  of  39, 
752,  and  38.     (Problem.) 


20 


ARITHMETIC. 


Review  Work. 

1.  46835 
29728 
42841 
56307 
92013 
52464 
27835 
12928 
52642 
83754 

Subtract : 

4.        142864 
-  92831 


2.  62423 

3.  36429 

18730 

72015 

29640 

49263 

19283 

52700 

76274 

29378 

<  53359 

42064 

84206 

19283 

19827 

87261 

52640 

36426 

64385 

92075 

5.        92053 
-  72935 


6.    -65842 
98375 


Write  results  only : 

8.    -5624 
9287 


7.        7329 
-4526 


9. 


—  1356 
2462 


10. 


2526 
—  1847 


Multiply  : 

11.   2846 
X59 


12.   3874 
X  78 


Write  results  only  : 

15.    2834         16.    595 
X  6  X  700 

Divide  : 

19.  2783  -f-  49 

20.  12064^62 

21.  13011 -T- 13 

22.  12094^56 


13.   9256         14.    6247 
X  206  X  125 


17.    1293  18.   463 

X  8  X  90 


23.  70943-f-29 

24.  5964  ^  87 

25.  29635 -T- 98 

26.  39305^70 


INDICATED  wo^lM^:  ..,:>         21 


Indicated  Work. 

NOTE.  —  The  pupil  should  be  required  to  read  his  indi- 
cated work. 

1.  4  +  3x2  =  ?  3.    4x3  +  2  =  ? 

2.  (4  +  3)  X  2  =  ?  4.    4  X  (3  +  2)  =  ? 

Teach  that  operations  indicated  by  the  signs  of  multi- 
plication and  division  should  be  performed  first,  unless 
the  parenthesis  is  used. 

Indicate  the  operations,  and  find  the  result. 

5.  4  increased  by  the  product  of  3  and  2. 

6.  The  sum  of  4  and  3,  multiplied  by  2. 

7.  The  product  of  4  and  3,  increased  by  2. 

8.  4  multiplied  by  the  sum  of  3  and  2. 

9.  84  less  the  product  of  5  and  6. 

10.  The  difference  between  72  and  42,  multiplied  by  4. 

11.  144  subtracted  from  the  product  of  18  and  18. 

12.  6  multiplied  by  the  difference  between  11  and  6. 

13.  Henry  has  58/  and  John  63/.     Charles  has  4  times 
as  much  as  both.     How  much  has  Charles  ? 

14.  Lucy  and  Mary  went  shopping.     Lucy  bought  lace 
for  55/,  and  Mary  5  yds.  of  ribbon  at  15/  a  yard.     What 
was  the  amount  of  both  purchases  ? 

15.  A  livery  man  bought  4  bu.  of  oats  at  $.40  a  bushel, 
and  a  load  of  hay  for  $12.     What  did  the  hay  and  oats 
cost? 

16.  Henry  had  75/.     He  bought  a  tablet  for  10/,  and 
paid  4/  apiece  for  6  pencils.     How  much  had  he  left  ? 

75/  -  (10/  +  6  X  4/). 

17.  Horace  travels  50  miles  and  Joseph  3  times  as  far. 
How  much  farther  does  Joseph  travel  than  Horace  ? 


22  ARITHMETIC. 

FRACTIONS. 
Oral  Work. 

One  of  the  two  equal  parts  of  an  apple  is  called  one  half 
of  an  apple.     One  half  is  written  £. 

One  of   the  two  equal  parts  of  a  number  is  £  of   the 
number. 

1.  How  many  are  £  of  4  oranges  ?     £  of  8  cows  ? 

2.  £  of  $10  are  how  many  dollars  ? 

One  of  the  three  equal  parts  of  an  apple  is  £  of  it. 

One  of  the  three  equal  parts  of  a  number  is  £  of  the 
number. 

3.  How  many  are  £  of  6  men  ?     £  of  12  men  ? 

4.  What  is  J  of  an  apple  ?     Illustrate. 

5.  What  is  £  of  any  number  ? 

6.  What  is  i  of  8  ?     i  of  12  ?     J  of  16  ? 

One  or  more  of  the  equal  parts  of  a  whole  is  a  Fraction. 

Divide  a  number  by  3  to  get  £  of  it. 

Divide  a  number  by  4  to  get  ^  of  it. 

How  do  you  get  J  of  a  number  ?     £  ?     f  ?     J  ? 

7.  Which  is  the  greater  part  of   an  apple,  £    or  J  ? 
Illustrate. 

8.  Which  is  the  greater  part  of  12,  £  or  £  ?    How  much 
greater  ? 

9.  When  you  have  found  J  of  a  number,  how  do  you 
find  f  ?  f  ?  f  ? 

10.  How  many  are  f  of  16  marbles  ?     Of  20  apples  ? 

11.  How  many  are  J  of  12  ?     |  of  12  ? 

12.  James  had  1  dollar,  and  Clara  |  of  a  dollar.     Which 
had  the  more  money  ?     Illustrate. 

13.  1  is  equal  to  I;  £;  |;  TV 

14.  2  is  equal  to  J ;  | ;  | ;  |. 


FRACTIONS. 


23 


Written  Work. 

1.  How  much  is  J  of  8  ?  16  ?  24  ?  32  ?  40  ? 

2.  Find  f  of  16.     £  of  24.     |  of  40. 

3.  Find  \  of  7,  14,  21,  28,  35. 

4.  Find  f  of  7,  14,  21,  28,  35. 

5.  How  much  is  J  of  15  ?     §  of  21  ? 

6.  Find  ^  of  10,  20,  30,  40,  50,  60,  70,  80,  90,  100  ? 

7.  Which  is  greater,  TL  of  40  or  £  of  30  ?    How  much  ? 

8.  Which  is  greater,  ^  of  100  or  J  of  40  ?    How  much  ? 

Oral  Work. 

1.  How  many  are  3  men  and  5  men  ?     4  horses  and 
6  horses  ? 

2.  How  much  are  3  sevenths  and  2  sevenths  ? 

3.  How  much  are  and 
4-      +     =    . 


6.  i  +  J  =  ? 

7-  T%  +  T15  = 

11.  *-?=? 

12.  -      =  ? 


8. 
9- 

10. 


13. 

14. 


15. 
16. 


Written  Work. 

1.  James  had  $J  and  George  $J.    How  many  cents  had 
both? 

2.  Mary  paid  £  of  a  dollar  for  a  book,  f  of  a  dollar  for 
a  hat,  and  J  of  a  dollar  for  gloves.     How  many  eighths  of 
a  dollar  did  she  spend  in  all  ? 

3.  How  much  is  2g  +  J  ?     3£  +  |  ?     6ft  +  A  ? 

4.  3}  5.      5-ft  6.      IT*,-  7.        15f 


24  ARITHMETIC. 

8.  A  lady  paid  $1|  for  a  book  and  $4J  for  a  hat.     How 
much  did  both  cost  ? 

9.  How  much  is  7§  —  J  ?     4|  —  |  ?     2^  —  ^  ? 

10.      6f  11.         8$  12.         15$         13. 

-3ft  —4^  —  6f 

Oral  Work. 

1.  (One-half  of  an  apple)  and  (one-half  of  an  apple) 
make  how  many  apples  ? 

2.  How  many  halves  in  a  whole  apple?     In  a  whole 
dollar  ?     In  any  whole  thing  ? 

3*     hlUf  +  half  ^  halves'       2  +  2  =  *• 

4.   Two  halves  of  an  apple  =  ?     5  =  ? 
7£_.?     J=?     $  =  ? 

o        lllll    t 

°*    3  ~r  3   i  $  —  5- 

9.    How  many  thirds  in  a  whole  apple  ? 

12.  How  many  thirds  in  4  ?     How  many  halves  in  3  ? 

13.  9  =  J.     10  =  £. 

Written  Work. 

1.  JU 6.  —  9  3      ^r_  __  9 

2.  J^  =  ?  4.     1^  =  ? 

Add: 

9.   4£  10.    7f  11.    8}  12.    5g 

5§                       6  5f  7| 

6|                       2J-  4f  4J 

13.    How  many   yards  in   3    pieces   of   silk   containing 
respectively  14|  yd.,  19|  yd.,  and  24 J  yd.  ? 


FEDERAL    MONEY.  25 

FEDERAL    MONEY. 

10  mills  (m.)  =  1  cent  (ct.). 
10  cents          =  1  dime  (di.). 
10  dimes         =  1  dollar  ($). 
10  dollars        =  1  eagle  (E.). 
20  dollars        =  1  double  eagle. 
Oral  Work. 

1.  How  many  dimes  in  6  dollars  ? 

2.  4  eagles  are  how  many  dollars  ? 

3.  A  man  had  $80  in  eagles.    How  many  eagles  had  he  ? 

4.  How  many  mills  in  15  cents  ? 

5.  In  5  dimes  how  many  cents  ? 

6.  A  dollar,  a  quarter,  a  dime,  and  a  nickel  are  how 
many  cents  ? 

7.  How  many  dollars  are  there  in  130  dimes  ? 

8.  How  many  dollars  are  there  in  1300  cents  ? 

9.  Divide  4  eagles  among  5  men.     How  much  would 
each  receive  ? 

10.    How  many  books  at  50/  each  can  be  bought  for  $2  ? 
Written  Work. 

1.  Reduce  2  dollars,  5  cents,  7  mills  to  mills. 

2.  J  of  3  double  eagles  are  how  many  cents  ? 

3.  Change  2971  mills  to  higher  denominations. 

4.  2000  dimes  are  how  many  dollars  ? 

5.  How  many  cents  are  there  in  $17J  ? 

6.  From  16  cents  take  9  mills. 

7.  If  you  had  a  quarter  of  an  eagle  and  spent  $1.75 
how  much  would  you  have  left  ? 

8.  270  cents  are  how  many  dimes  ? 

9.  How  many  five-cent  pieces  in  a  box  containing  $20  ? 


26  ARITHMETIC. 

DRY  MEASURE. 

2  pints  (pt.)  =  1  quart  (qt.). 
8  qt.  =1  peck  (pk.). 

4  pk.  =  1  bushel  (bu.). 

36  bu.  =  1  chaldron  (chal.). 

Oral  Work. 

1.  How  many  pecks  in  9  bushels  ? 

2.  In  22  pints  how  many  quarts  ? 

3.  A  bushel  of  apples  at  $.25  a  peck  will  cost  what  ? 

4.  How  many  pints  are  in  6  qt.  1  pt.? 

5.  What  will  a  peck  of  chestnuts  bring  if  sold  at  10/ 
a  quart  ? 

6.  How  many  times  can  a  quart  cup  be  filled  from  a 
bushel  of  walnuts  ? 

7.  How  many  quarts  are  in  9  pecks  ? 

Written  Work. 

1.  Eeduce  15  pk.  7  qt.  to  pints  ? 

2.  How  many  quarts  are  in  846  pints  ? 

3.  Henry  gathered  16  bu.  2  qt.  of  walnuts,  and  sold 
them  at  f .  08  a  quart.     What  did  he  receive  for  them  ? 

4.  In  8136  pt.  how  many  bushels,  etc.? 

5.  What  will  6  bu.  2  pk.  of  cranberries  be  worth  at 
f  .75  a  peck  ? 

6.  How  many  quarts  are  there  in  7  bu.  3  pk.  7  qt.? 

7.  A  peck  of  peaches  were  sold  from  a  crate  containing 
a  bushel.     How  many  quarts  were  left  ? 

8.  How  many  bushels  are  there  in  576  pints  ? 

9.  14  bushels  of  oats  will  last  a  horse  how  many  weeks 
if  he  is  fed  8  qt.  a  day  ? 

10.    What  will  32  pk.  of  walnuts  bring  at  f  .05  a  pint  ? 


LIQUID   MEASURE.  27 

LIQUID   MEASURE. 

4  gills  (gi.)  =  1  pint  (pt.). 

2  pt.  =  1  quart  (qt.). 

4  qt.  =1  gallon  (gal.). 

31i  gal.  =  1  barrel  (bbl.). 

2  bbl.  =  1  hogshead  (hhd.). 

2  hhd.  =  1  pipe  (pi.). 

2  pi.  =1  tun. 

Oral  Work. 

1.  How  many  pint  cups  can  be  filled  from  8  quarts  ? 

2.  A  quart  of   milk  was  taken  from  a  five-gallon  pan 
How  much  was  left  ? 

3.  How  many  gallons  in  a  hogshead  ? 

4.  |  of  a  gallon  are  how  many  quarts  ? 

5.  How  many  hogsheads  will  8  barrels  of  oil  fill  ? 

6.  A  family  uses  2  qt.  of  milk  a  day.     What  will  the 
milk  bill  amount  to  in  a  week  at  the  rate  of  4/  a  quart  ? 

7.  How  many  quarts  are  there  in  7  gal.  3  qt.  ? 

Written  Work. 

1.  Reduce  1  bbl.  to  gills. 

2.  2%  gallons  of  kerosene  at  2?  a  pint  will  cost  what  ? 

3.  Paid  $1.60  for  cider  at  $.05  a  quart.      How  many 
gallons  were  purchased  ? 

4.  Change  711  gills  to  higher  denominations. 

5.  How  many  2-quart  cups  can  be  filled  from  a  barrel 
of  sirup  ? 

6.  Change  7  gal.  2  qt.  1  pt.  to  gills. 

7.  In  276  pints,  how  many  gallons  ? 

8.  A  merchant  paid  $10  for  a  barrel  of  molasses,  and 
retailed  it  at  $.40  a  gallon.     What  was  his  gain  ? 


28  ARITHMETIC. 

9.    A   half-barrel   of  vinegar  was  sold   at  2/  a  quart. 
What  was  received  for  it  ? 

10.  How  many  gallons  in  16  quarts  ? 

11.  13£  gallons  have    been  sold  from  a  barrel.     How 
many  quarts  are  left? 

12.  At  7/  a  quart  what  will  15  gal.  of  vinegar  cost  ? 

AVOIRDUPOIS   WEIGHT. 

16  drams  (dr.)  =  1  ounce  (oz.). 

16  oz.  =  1  pound  (lb.). 

25  lb.  =  1  quarter  (qr.). 

4  qr.  =1  hundred  weight  (cwt.). 

20  cwt.  =  1  ton  (T.). 

2000  lb.  =  1  ton. 

Oral  Work. 

1.  How  many  ounces  are  in  4  pounds  ? 

2.  In  32  drams,  how  many  ounces  ? 

3.  What  will  a  pound  of  candy  cost  at  $.02  an  ounce  ? 

4.  How  many  pounds  in  4  tons  ? 

5.  In  6000  lb.  how  many  tons  ? 

6.  How  many  pounds  are  in  a  hundred  weight  ? 

7.  Paid  $.48  a  pound  for  candy.     How  much  is  that  an 
ounce  ? 

8.  How  many  3-pound  packages  can  be  made  from  75 
pounds  of  coffee  ? 

Written  Work. 

1.  How  many  ounces  are  there  in  25  lb.  ? 

2.  In  1\  tons,  how  many  pounds  ? 

3.  How  many  bullets  weighing  2  oz.  each  can  be  made 
from  32  lb.  4  oz.  of  lead  ? 

4.  Eeduce  18  lb.  7  oz.  to  drams. 


AVOIRDUPOIS   WEIGHT.  29 

5.  What  will  2£  Ib.   dried  peaches  cost  at  $.32  per 
pound  ? 

6.  In  1364  drams,  how  many  ounces  ? 

7.  Five  boys  share  equally  1  Ib.  9  oz.  of  candy.     What 
is  each  boy's  share  ? 

8.  How  many  4-ounce  bags  can  I  fill  from  a  box  hold- 
ing 7£  Ib.  of  candy  ? 

9.  What  is  the  difference  in  ounces  between  a  hundred 
weight  and  97£  pounds  ? 

10.  What  will  7f  Ib.  of  indigo  cost  at  $ .03  an  ounce  ? 

11.  Keduce  18  Ib.  4  oz.  to  drams. 

12.  A  hundred  weight  is  what  part  of  a  ton  ? 

LINEAR   MEASURE. 
12    inches  (in.)  =  1  foot  (ft.) 
3    ft.  =1  yard  (yd.) 

5%  yd.  =  1  rod  (rd.) 

Oral  Work. 

1.  How  many  inches  long  is  a  yard  stick  ? 

2.  Reduce  2  ft.  4  in.  to  inches. 

3.  24  feet  are  how  many  yards  ? 

4.  How  many  feet  around  a  picture  2  ft.  long  and  1  ft. 
wide  ? 

5.  How  many  inches  in  a  half-yard  ? 

6.  At  $.16  a  yard  what  will  1£  yd.  of  ribbon  cost  ? 

7.  6  f t.  +  2  ft.  +  4  ft.  are  how  many  yards  ? 

8.  How  many  feet  in  108  inches  ? 
Written  Work. 

1.  A  rod  is  how  many  feet  ? 

2.  In  124  inches,  how  many  yards,  etc.  ? 

3.  Reduce  14  ft.  7  in.  to  inches. 


30  ARITHMETIC. 

4.  Change  1848  in.  to  feet. 

5.  How  many  feet  in  16  yards  ?     In  118  yards  ? 

6.  What  will  be  the  cost  of  16  yd.  of  wire  at  2/  a  foot  ? 

7.  How  many  yards  around  a  room   18   ft.  long  and 
15  ft.  wide  ? 

8.  At  $.36  a  yard  what  will  18  inches  of  cord  cost  ? 

9.  A  pole  119  ft.  high  is  broken  off  27  ft.  from  the 
bottom.     How  many  yards  are  broken  off  ? 

10.  How  many  inches  remain  ? 

11.  What  will  it  cost  to  build  12  yards  of  fence  at  $.42 
a  foot  ? 

12.  A  picture  is  72  inches   long  and  36  inches  wide. 
How  many  feet  in  the  frame  around  it  ? 

ADDITION  AND  SUBTRACTION  OF  DENOMINATE 
NUMBERS. 

Add  :       7  bu.  1  pk.  3  qt.  6  bbl.     7  gal.  1  qt. 

10         1          2  5          12          1 

412  461 

1  yd.  2  ft.    6  in.  4  bbl.     7  gal.  4  qt.  1  pt. 

21  62  1 

123  3  511 


Find  the  sum  : 

1.  3  bu.  2  pk.  2  qt.  1  pt. ;      4  bu.  5  pk.  3  qt. ;      7  bu. 
1  pk.  4  qt.  1  pt. 

2.  7  Ib.  8  oz.  6  dr. ;     4  Ib.  11  oz.  5  dr.  ;     2  Ib.  4  dr. 

3.  Ibbl.  14  gal.  2  qt.  Ipt.;    2  bbl.  5  gal.  3qt.;    7  gal. 
3  qt. 

4.  4  yd.  2  ft.  7  in.  ;     5  yd.  1  ft,  6  in. ;     2  yd.  11  in. 

5.  16  Ib.  10  oz.  3  dr. ;     9  Ib.  7  oz.  ;     5  Ib.  14  dr. 


COMPOUND  ADDITION   AND   SUBTRACTION.  31 

Subtract : 

1.    16  Ib.  8  oz.  3  dr.                   2.    7  yd.  3  ft.  9  in. 
542  2 5        7 

3.    16  da.  5  hr.  36  min.             4.    27  gal.  3  qt.  1  pt.  2  gi. 
5         7        18  _18 213 

5.  From  6  dol.  7  di.  2  ct.  3  m.  take  4  dol.  5  di.  8  ct.  1  m. 

6.  Find  the  difference  between  4  Ib.  8  oz.  3  dr.  and  2  Ib. 
5  oz.  7  dr. 

7.  From  a  can  containing  7  gal.  2  qt.  1  pt.  of  milk,  4 
gal.  3  qt.  were  sold.     How  much  was  left  ? 

8.  6  ft.  11  in.  were  cut  from  a  pole  18  ft.  9  in.  long. 
How  long  was  the  pole  then  ? 

9.  Into  a  barrel  were  put  16  gal.  3  qt.  1  pt.  of  oil  one 
day,  3  gal.  3  qt.  the  next,  and  7  gal.  1  pt.  the  next.     How 
much  oil  was  there  in  the  barrel  ? 

10.  9  Ib.  8  oz.  of  candy  were  sold  from  a  box  containing 
14  Ib.     How  much  was  left  ? 

11.  A  4-gallon  pail  and  a  quart  bottle  were  filled  from  an 
8-gallon  cask  of  cider.     How  much  was  left  ? 

12.  How  much  twine  is  there  in  3  balls  if  there  are  16  yd. 
1  ft.  in  one,  17  yd.  2  ft.  8  in.  in  another,  and  9  yd.  2  ft.  11 
in.  in  the  third  ? 

Oral  Work. 

1.  From  a  4-gallon  jug  2  qt.  were  taken.     How  much 
was  left  ? 

2.  8  oz.  were  sold  from  a  box  of  candy  holding  5  Ib. 
How  much  was  left  ? 

3.  A  boy  cut  2  ft.  from  a  piece  of  twine  4  yd.  long 
How  much  was  left  ? 

4.  From  5  Ib.  7  oz.  take  2  Ib.  5  oz. 


32  ARITHMETIC. 

GENERAL   REVIEW  PROBLEMS. 

1.  At  $1.50  a  yard,  what  will  64  yd.  of  carpet  cost  ? 

2.  A  man  earns  $65  a  month,  and  spends  $31.     How 
long  will  it  take  him  to  save  $238  ? 

3.  What  is  |  of  2080  pounds  ? 

4.  Add  1,  £,  and  f . 

5.  Write  in  figures  seven  hundred  dollars  six  mills. 

6.  Two  boys  skate  in  the  same  direction.     One  goes  65 
yd.  and  the  other  3  times  as  far.     How  far  apart  are  they 
then  ?     (Illustrate.) 

7.  Find  the  quotient,  using  2734  and  15. 

8.  How  many  pints  of  walnuts  can  be  sold  from  5  bu. 
2pk.  ? 

9.  Multiply  six  thousand  four  hundred  seventy-three  by 
sixty-nine. 

10.  Charles  has   $42.      James  has  2£  times  as  much. 
How  much  money  have  both  ? 

11.  Find  the   difference   between   £   of   714   and   $   of 
1456. 

12.  Florence  bought  6  dozen  eggs  at  $.32  a  dozen  and  2 
dozen  oranges  at  $.02  apiece.     What  did  all  cost  ? 

13.  A  man  bought  a  horse  for  $110  and  a  harness  for 
$30.     He  paid  J  as  much  as  both  cost  for  a  wagon.     What 
did  the  wagon  cost  ? 

14.  At  $.18  a  peck  what  will  6  bu.  of  apples  cost? 

15.  Find  the  product  of  6  X  7  X  3  X  9. 

16.  A  farmer  bought  goods  to  the  amount  of  $6.     He 
paid  |  of  it  in  oats.     How  much  money  did  he  have  to 
pay? 

17.  James  paid  $19.75  from  a  roll  of  bills  containing 
$40.     How  much  was  left  ? 


KEVIEW.  33 

18.  A  lot  which  cost  $125  was  sold  at  a  gain  of  £  of  its 
cost.     What  was  received  for  it  ? 

19.  From  180  take  f  of  itself. 

20.  288  Ib.  of  coffee  will  fill  how  many  12-pound  bags  ? 

21.  At  27/  a  pound  what  will  three  30-pound  jars  of 
butter  cost  ? 

22.  If  5  dozen  of  eggs  cost  $1.20,  what  will  %  a  dozen 
cost? 

23.  Take  2099  from  7809. 

24.  Find  the  sum  of  T5r  of  132  and  }  J  of  132. 

25.  2  Ib.  4  oz.  of  candy  at  $.03  an  ounce  will  cost  what  ? 

26.  A  lady  who  had  $100  bought  a  shawl  for  $30,  and 
paid  $2  a  yard  for  18  yd.  of  silk.    How  much  had  she  left  ? 

27.  Add  $16.29  ;  $2.71 ;  $.49 ;  $238  ;  $16.12 ;  and  $42. 

28.  How  many  feet  around  a  square  table  that  is  18  in. 
on  a  side  ?     (Illustrate.) 

29.  In  what  year  was  a  man  born  if  his  age  is  now  38  ? 

30.  A  boy  earns  $4.20  a  week.     What  will  he  earn  in 
10  days  ? 

31.  What  is  the  cost  of  9  books  at  $J  each  and  £  dozen 
pictures  at  $2£  each  ? 

32.  If  9  dozen  of  oranges  cost  $1.53,  what  will  12  dozen 
cost? 

33.  $96  —  $.45  =  ? 

34.  249  X  74  =  ? 

35.  Add  726,  9463,  95,  18263,  9295,  38640,  1872,  and 
575. 

36.  At  $3|  a  ton  what  will  3$  tons  of  coal  cost  ? 

37.  The  dividend  is  31232.    The  divisor  is  32.    Find  the 
quotient. 


84  ARITHMETIC. 

38.  If  milk  is  4/  a  quart,  how  many  gallons  can  be  pur- 
chased for  $1.92  ? 

39.  If    six  tons  of    hay  cost  $84,  how  many  tons  will 
$252  buy  ? 

40.  How  many  pints  in  18  bu.? 

41.  If  a  dozen  pencils  cost  $.10  what  will  3  boxes,  each 
containing  6  dozen,  cost  ? 

42.  8  boys  each  received  $|.     How  many  dollars  did  it 
take? 

43.  From  J  of  the  sum  of  297  and  313  take  £  of  their 
difference. 

44.  If  you  paid  $8£  for  a  coat,  $2j  for  a  hat,  and  $5  for 
boots,  what  did  all  cost  ? 

45.  Divide  37958  by  91. 

46.  Mr.  Sherwood  paid  $1250  for  a  lot,  built  a  house  for 
$4275,  and  a  barn  for  $1025.     He  sold  it  all  for  $9000. 
What  was  his  profit  ? 

47.  Add  813,  9257,  8564J,  267,  and  9043£. 

48.  A  man  divided    $400    equally  among   his   5    sons. 
One  spent  g  of  his  share  for  books.     What  did  the  books 
cost? 

49.  Add  §  of  $.63,  i  of  $1,  £  of  $48,  and  £  of  $.42. 

50.  Eeduce  1  hhd.  to  gills. 

51.  Take  2837  from  19364. 

52.  Add  eleven  thousand  three  hundred  sixty-nine  ;  four 
thousand  thirty-nine  ;  seventy-eight  thousand  four  hundred 
fifteen  ;  four  hundred  eighty  thousand  five  hundred  seventy- 
three  ;  twelve  thousand  sixty-four. 

53.  When  milk  is  5/  a  quart,  what  will  it  cost  a  family 
for  13  weeks  if  14  qt.  a  week  are  used  ? 

54.  How  many  thirds  in  15  ? 


EEVIEW.  35 

55.  A  room  is  28  ft.  wide  and  32  ft.  long.     How  many 
yards  around  it  ?     (Illustrate.) 

56.  Paid  $34  for  8  tons  of  coal.     What  was  it  a  ton  ? 

57.  A  man  paid  $6  apiece  for  18  sheep,  and  had  $78 
left  in  his  pocket.     How  much  had  he  at  first  ? 

58.  How   many   pages    are   there    in  17    books  of  267 
pages  each  ? 

59.  Divide  2083  by  19. 

60.  14812  -^  47  =  ? 

61.  Divide  three  thousand  eight  hundred  seventy-four  by 
twenty-six. 

62.  |  of  75  gal.  of  molasses  were  sold  at  $.18  a  quart. 
How  much  was  received  for  it  ? 

63.  Add  213,  8237,  5164,  291,  9168,  3792,  and  847. 

64.  Divide  $325  equally  among  13  men.     What  would 
each  receive  ? 

65.  From  7980  take  4518. 

66.  The  minuend  is  12138,  the  subtrahend  1497.     Find 
the  difference. 

67.  Add   $11.08,  $213,  $9.643,    $.876,    $538.275,    and 


68.  137  oranges  were  sold  from  a  box  containing  225. 
What  would  they  bring  at  $.04  each  ?     The  rest  were  sold 
at  $.05  apiece.     What  did  they  bring  ? 

69.  Express  in  words  3130019. 

70.  How  many  pints  in  75  gal.  3  qt.  ? 

71.  Two  men  are  327  miles  apart.     They  travel  towards 
each  other,  one  going  95  miles  and  the  other  73.     How  far 
apart  are  they  then  ? 

72.  Take  six  thousand   eight   hundred   forty-two   from 
eleven  thousand  two. 


36  ARITHMETIC. 

73.  How  many  dimes  in  17  dollars  ? 

74.  The    multiplicand   is    573    and    the   multiplier   38. 
Find  the  product. 

75.  A  man  who  earned  $1050  a  year,  spent  |  of  it  for 
rent.     What  did  his  rent  amount  to  in  5  years  ? 

76.  Mr.  Jones  has  945  sheep  in  one  lot  and  J  as  many  in 
another.     How  many  sheep  in  both  lots  ? 

77.  Take  $.38  from  $38. 

78.  Write  a  number  of  three  groups. 

79.  Write  a  number  of  two  groups.     Find  the  difference 
between  the  two  numbers. 

80.  Add  $17£,  $9,  $6f ,  $14£,  $8J,  and  $.18. 

81.  John  has  26  marbles.     Fred  has  16  more  than  twice 
as  many.     How  many  marbles  have  both  ? 

82.  4216  -r-  15  =  ? 

83.  How   many   years    since   America   was    discovered 
in  1492? 

84.  At  $24  a  ton  what  will  263  tons  of  hay  cost  ? 

85.  How  many  pounds  in  218  ounces  ? 

86.  A  barrel  of  flour  weighs  196  pounds.     How  many 
pounds  in  3  J  barrels  ? 

87.  A  fruit  dealer  bought  5  dozen  boxes  of  berries  for 
$4.75  and  sold  them  for  $.09  a  box.     What  did  he  gain  ? 

88.  Bought  9  yd.   of  cloth  at  $1.75  a  yard  and  paid 
$13.50  for  making   and  trimmings   of   dress.     What   did 
it  cost  ? 

89.  Two  cities  are   540   miles   apart.     How  fast   must 
a  train  run  to  make  the  distance  in  18  hours  ? 

90.  A  clerk's  salary  is  $900  a  year.     He  spends  f  of  it. 
How  much  does  he  save  in  a  month  ? 

91.  }   of   the  oranges    in   a   box   containing   300    were 


BEVIES 

divided  equally  among   5   persons.     How  many  did  each 
receive,  and  how  many  were  left  in  the  box? 

92.  A  merchant  who  had  72  barrels  of  sugar  sold  |  of 
them  to  one  customer,  £  to  another,  and  f  to  another.    How 
many  barrels  had  he  left  ? 

93.  How  many  lemons  in  3  loads,  28  boxes  on  each  load 
and  100  lemons  in  a  box  ? 

94.  Two  men  travel  from  the  same  place  in  opposite 
directions.     One  goes  18  miles    a   day  and  the  other  27. 
How  far  apart  are  they  at  the  end  of  4  days  ?     (Illustrate.) 

95.  A  boy  wishes  to  buy  a  bicycle  for  $60.     He  has 
$42,  and  earns  $.75  a  week  for  6  weeks.     How  much  does 
he  still  need  ? 

96.  8  men  were  paid  $96  for  6  days'  work.     How  much 
was  that  a  day  for  one  man  ? 

97.  Find  £  of  $122. 

98.  What  will  10  eggs  cost  at  $.24  a  dozen  ? 

99.  21432  -  947  =  ? 

100.  If  you  had  $7J,  and  spent  $5J,  how  much  would 
you  have  left  ? 

101.  A  farmer  had  a  horse  worth  $265,  and  he  exchanged 
it  for  a  yoke  of  oxen  and  two  cows.     The  oxen  he  sold  for 
$118,  and  one  cow  for  $75,  the  other  for  $54.     What  was 
his  loss  ? 

102.  A  man  paid  $21  for  a  stove  and  £  as  much  for 
a  chair.     What  did  both  cost  ? 

103.  Multiply  627  by  94. 

104.  The  minuend  is  1362,  the  difference  584.     What  is 
the  subtrahend  ? 

105.  How  many  quarts  of  oats  can  be  put  in  35  peck 
measures  ? 


38  ARITHMETIC. 

106.  Express  in  figures  two  million,  three  hundred  sev- 
enteen thousand,  five. 

107.  642  +  89  +  97  +  7362  +  745  +  469  +  1286  =  ? 

108.  $3.12  -f-  4  =  ?     (Problem.) 

109.  Write  the  present  year  in  figures.     In  words.     In 
Roman. 

110.  What  will  3  bu.  of  peanuts  cost  at  $ .05  a  pint. 

111.  4829  -T-  16  =  ? 

112.  J  of  $2440  =  ? 

113.  What  must  be  added  to  816  to  make  1003  ? 

114.  A  man  receives  $658   rent  a  year  for  one  store, 
$497  for  another,  and  $276  for  a  third.     What  does  he 
receive  in  rents  for  three  years  ? 

115.  From  the  sum  of  1216  and  1890  take  their  difference. 

116.  A  piano  worth  $162  was  sold  for  f  of  its  value. 
What  was  received  for  it  ? 

117.  The  product  of  two  numbers  is  216.     One  of  the 
numbers  is  18.     What  is  the  other  ? 

118.  317  x  56  =  ? 

119.  What  is  56  in  the  preceding  example  ? 

120.  How  long  would  a  bin  of  oats  last  17  horses  if  it 
would  last  one  horse  391  days  ? 

121.  27934  +  54  =  ? 

122.  If  8  men  earn  $96  a  week,  what  will  6  men  earn  ? 

123.  How  many  bushel  measures  can  be  filled  from  640 
pt.  of  oats  ? 

124.  Find  the  product  of  1826  and  89. 

125.  1912  -  498  -  156  =  ? 

126.  At   5/   an    oz.    what   will    4    Ib.    5    ounce    cloves 
cost? 


REVIEW.  39 

127.  Dr.  Stokes  sold  his  horse  for  $195,  and  lost  $45. 
What  did  the  horse  cost  ? 

128.  Find  f  of  $2142. 

129.  A  grocer  bought  9  bu.  of  apples  for  $9,  and  sold 
them  at  the  rate  of  $.30  a  peck.     What  did  he  gain  ? 

130.  How  much  more  than  J  of  280  is  f  of  1535  ? 

131.  9  gal.  3  qt.  of  milk  will  fill  how  many  quart  cups  ? 

132.  If  $3£  will  buy  7  books,  what  will  a  dozen  cost  ? 

133.  10£  bu.  of  cherries  at  6^  a  quart  will  cost  what  ? 

134.  $2.87  +  $32.90  +  $.15  +  $921.83  +  $16.74  =  ? 

135.  To  384  add  |  of  it. 

136.  £  of  18  ft.  of  cord  are  cut  on.     How  many  yards 
are  left  ? 

137.  How  much  money  would  a  lady  have  left  if  she  had 
a  five-dollar  bill  and  spent  J  of  it  ? 

138.  Paid  $45.90  for  9  tons  of  coal.    What  was  it  a  ton  ? 

139.  How  much  can  a  boy  save  in  13  weeks  if  he  saves 
5  cents  a  day  ? 

140.  How  many  feet  around  a  table  1  yard  square  ? 

141.  What  will  £  a  bushel  of  walnuts  cost  if   2   bu. 
cost  $4  ? 

142.  Frank  had  $30.18,  Rose  had  half   as  much,  and 
James  twice  as  much.     How  much  money  had  the  three  ? 

143.  6943  -v-  76  =  ? 

144.  The  sum  of  two  numbers  is  7315.    One  of  the  num- 
bers is  5817.     What  is  the  other  ? 

145.  A  boy  ate  J  of  a  pie.     What  part  of  it  was  left  ? 

146.  A  man  who  had  $5  spent  £  of  it  for  a  book,  and 
the  rest  for  a*  hat.     What  did  the  hat  cost  ? 

147.  What  will  $J  +  ${  +  $$  +  $J  amount  to  ? 


40  ARITHMETIC. 


148.  How  many  oranges  in  18£  dozen  ? 

149.  Add  2|,  6J,  7J,  9,  and  17J. 

150.  Find  the  product  of  4129  and  37. 

151.  At  2/  an  ounce  what  will  1£  Ib.  candy  cost  ? 

152.  Write  in  words  92073460. 

153.  How  many  pieces  of  wood  3  in.  long  will  a  45-foot 
pole  make  ? 

154.  Bought  nuts  for  $.06  a  quart.    What  did  7  bu.  cost  ? 

155.  (916  +  159  -  187  -  213)  X  0  =  ? 

156.  If   the  divisor  is  178  and  the  quotient  123,  what 
is  the  dividend  ? 

157.  From  }£  take  ft- 

158.  A  boy  bought  a  pair  of  skates  for  $3£,  and  sold 
them  for  $2J.     What  did  he  lose  ? 

159.  8  times  the  cost  of  a  book  is  $22.     What  did  the 
book  cost  ? 

160.  Find  ft  of  $132. 

161.  If  i  a  yard  of  cloth  costs  $2,  what  will  5  yd.  cost  ? 

162.  How  many  cents  in  6  eagles  ? 

163.  A  gallon,  2  quarts,  and  a  pint  are  how  many  pints  ? 

164.  ^  =  ?     f  J  =  ?     f  f  =  ? 

165.  From  the  sum  of  8137  and  12291  take  1986. 

166.  Add  173,  8164,  97,  7931,  8,  9014,  and  178. 

167.  £  of  the  oil  in  a  barrel  was  sold.     How  many  quarts 
were  left  ? 

168.  What  part  of  3  pk.  is  12  qt.  ? 

169.  Multiply  $18.065  by  14. 

170.  A  man  who  had  $16|  spent  $9|.     How  much  had 
he  left  ? 

171.  384  pt.  are  how  many  gallons  ? 


ADDITION. 


41 


Add: 

1. 

4287 

2.  7236 

3.  62345 

5965 

1834 

18376 

8473 

3529 

29046 

4287 

9287 

92043 

3069 

5078 

87536 

4218 

9217 

42365 

9246 

3465 

17393 

3287 

2974 

24867 

7249 

3826 

63587 

2756 

9375 

20624 

8461 

5468 

85626 

3097 

2083 

13346 

Add: 

4. 

$173.25 

5.  $  836.427 

6.  $7000.42 

92.47 

1521.500 

83.92 

9.38 

936.008 

6214.836 

407.25 

42.53 

807.015 

92.16 

1006.279 

78.26 

57.84 

83.442 

9287.426 

9.26 

64.297 

383.527 

Subtract  : 

1. 

27134 

2.  18307 

3.   5645 

9862 

11409 

17013 

4. 

2365 

5.  8034 

6.  127421 

9271 

7296 

86456 

7.  From  9864  take  3286. 

8.  10016  -  9284  =  ? 

Add: 

9.  42J    10.  63j    11. 
131 


12. 


42 


ARITHMETIC. 


1. 

27938 

-57 

—.  9 

2. 

62941 

-83 

==  9 

3. 

7209 

-18 

=  9 

4. 

8312 

-83 

_  9 

5. 

64205 

-42 

o 

6. 

17483 

-56 

_  9 

7. 

29006 

-29 

=  9 

8. 

18736 

-54 

__  9 

9. 

56803 

-92 

=  9 

10. 

9063 

-50 

9 

11.  6284  —  59  =  ? 

12.  92307  —  36  =  ? 

13.  53124  —  72  =  ? 

14.  96503  —  87  =  ? 

15.  600412  —  29  =  ? 

16.  37561  -  46  =  ? 

17.  25964  -  38  =  ? 

18.  40136  —  24  =  ? 

19.  50601  -f-  97  =  ? 

20.  80319  -g-  75  =  ? 


Indicated  Work. 

(Indicate  the  operation,  and  give  result.) 

1.  James  had  $.75  and  spent  $.32  for  a  book  and  $.18 
for  paper.     How  much  had  he  left  ? 

2.  A  man  who  owed  $500  paid  $275  and  then  borrowed 
$132  more.     How  much  did  he  owe  then  ? 

3.  Laura  bought  3  yd.  of  ribbon,  paying  $.18  a  yard. 
How  much  change  would  she  receive  from  a  dollar  ? 

4.  John  skated  72   yards  and   Henry  3  times  as  far. 
How  far  apart  were   they  if   they  went  in  the  same  di- 
rection ? 

5.  John  had  $27  in  the  bank  and  drew  out  $4.25.     He 
then  deposited  $18.     How  much   money  had  he  in   the 
bank? 

6.  Julia  had  $.75  and  her  sister  3  times  as  much.    How 
much  money  had  both  ? 

7.  A  merchant  has  3  pieces  of  cloth,  each  containing  24 
yards.     He  sells  18  yd.  one  day  and  41  the  next.     How 
much  has  he  left  ? 

8.  Jennie  bought  a  book  for  $.36  and  gloves  for  $.75. 
How  much  change  would  she  receive  from  a  five-dollar 
bill? 


REVIEW. 

Oral  Work. 

1.  Our  school  term  is  20  weeks  long.     If  we  have  two 
holidays,  how  many  days  do  we  attend  school  ? 

2.  f  of  12  is  what  part  of  16  ? 

3.  A  pint  of  water  is  poured  into  a  gallon  measure,  and 
the  measure  is  then  filled  with  milk.     How  much  milk 
is  in  it  ? 

4.  If  3  oranges  cost  10  cents,  how  many  can  I  buy  for 
$.20? 

5.  There  are  23  girls  and  27  boys  present.     How  many 
scholars  are  in  the  school-room  ? 

6.  Fred  paid  $90  for  a  bicycle  and  sold   it  for  $75. 
How  much  did  he  lose  ? 

7.  How  many  oranges  at  $.04  each  can  you  get  for  2 
dimes  ? 

8.  3  hats  at  $5  each  and  5  umbrellas  at  $3  each  will 
cost  what  ? 

9.  f  of  a  pie  is  eaten.     What  part  is  left  ? 

10.  How  many  yards  in  27  ft.? 

11.  At  5/  each  what  will  40  tablets  cost  ? 

12.  Ten  eggs  out  of  5  dozen  are  bad.     How  many  are 
good  ? 

13.  From  3£  take  1£. 

14.  From  a  •  cistern  containing  25  bbl.  of   water  9  bbl. 
leaked  out.     How  much  was  left  ? 

15.  A  lady  bought  8  Ib.  of  meat  at  $.12  a  pound,  and 
gave  the  butcher  a  dollar  bill.     How  much  change  did  she 
receive  ? 

16.  Take  f  of  12  from  30. 

17.  3  books  at  $.50  each  would  cost  what  ? 

18.  How  many  feet  in  36  inches  ? 


44  ARITHMETIC. 

1.  At  $19.50  a  ton  find  the  cost  of  12000  Ib.  of  hay. 

2.  In  68  oz.  how  many  pounds  ? 

3.  A  cistern  holds  14  bbl.  3  gal.  2  qt.  of  water.     If  7 
bbl.  3  qt.  are  taken  out,  how  much  is  left  ? 

4.  The  subtrahend   is  63281,  the  difference  is   41263. 
Find  the  minuend. 

5.  Find  the  cost  of   a  hogshead  of   molasses  at  $.15 
a  quart. 

6.  10080^32. 

7.  2J  +  }  +  5  +  6J  +  8}  =  ? 

8.  How  many  drams  in  3  Ib.  12  oz.  9  dr.  ? 

9.  $16.755  +  $1.20  +  $.45  +  $.008  +  $7.015  +  $.602 
+  $25  =  ? 

10.  How  much  fence  would  be  needed  to  inclose  a  lot  72 
ft.  by  58  ft.  ? 

11.  How  many  hogsheads  will  it  take  to  hold  10710  gal. 
of  molasses  ? 

12.  Which  is  the  greater  amount  of  money,  ^  of  $350  or 
}  of  $630.27  ?     How  much  greater  ? 

13.  125J  -  86J  =  ? 

14.  How  many  yards  of  tape  will  it  take  to  go  around  a 
table  3  ft.  long  and  5  ft.  wide  ? 

15.  If  you  pay  $.25  apiece,  how  many  books  can  you  get 
for  $9  ? 

16.  At  $.16  a  gallon,  how  many  gallons  of  vinegar  will 
pay  for  6  Ib.  of  butter  at  $.32  a  pound  ? 

17.  Write  and  add  all  the  numbers  between  7  and  50 
that  end  in  the  figure  8. 

18.  How  many  times  can  16  be  subtracted  from  1328  ? 

19.  At  8/  a  pound  what  will  4£  Ib.  of  meat  cost  ? 

20.  What  will  20£  bu.  of  tomatoes  bring  at  $.40  a  bushel  ? 


MISCELLANEOUS.  45 

21.  How  many  pounds  in  526  ounces  ? 

22.  A  horse  and  $125  were  given  for  a  carriage  valued 
at  $270.     What  was  the  horse  worth  ? 

23.  Draw  a  square,  and  call  each  side  15  ft.    How  many 
inches  half  way  around  the  square  ?      How  many  yards 
around  the  other  half  ? 

24.  If  6  men  can  do  some  work  in  12  days,  how  long 
will  it  take  one  man  to  do  it  ?     How  long  will  it  take 
8  men? 

25.  28  horses  cost  $6944.     What  is  the  cost  of  one  ? 

26.  How  many  inches  in  4  yd.  2  ft.  9  in.? 

27.  Reduce  ajf 4  to  a  whole  number. 

28.  7  bbl.  were  pumped  from  a  cistern  holding  41  bbl. 
16  gal.     How  much  was  left  ? 

29.  At  $.28  a  pound,  what  will  be  the  cost  of  16 J  pounds 
of  coffee  ? 

30.  If  4  men  earn  $64  in  a  week,  how  much  can  13  men 
earn  in  the  same  time  ? 

31.  36741  -r-  92  =  ? 

32.  The  sum  of  two  numbers  is  8013.     One  of  the  num- 
bers is  2416.     What  is  the  other  ? 

33.  If  8  tons  of  coal  cost  $42,  what  will  1  ton  cost  ? 

34.  In  how  many  weeks  will  a  family  use  196  qt.  of  milk, 
if  2  qt.  a  day  are  used  ? 

35.  How  many  yards  of  ribbon  at  $.24  a  yard  can  be 
bought  for  $2.88  ? 

36.  How  many  quarts  in  £  of  a  barrel  ? 

37.  7£  bu.  of  nuts  at  6/  a  quart  will  cost  what  ? 

38.  From  9}f  take  6T\. 

39.  Add  three  hundred  seventeen  thousand  four  hundred 
six ;    nine    million   twenty-three    thousand   eight   hundred 


46  ARITHMETIC. 

fifteen  ;    forty-five  thousand  four  hundred  eighty-six ;    six 
hundred  nine  thousand  thirty. 

40.  A  man  carried  in  3  tons  of  coal  in  a  basket  holding 
40  pounds.     How  many  basketfuls  did  he  carry  ? 

41.  How  many  times  would  you  fill  a  quart  cup  to  empty 
a  barrel  ? 

42.  If  17  Ib.  of  butter  cost  $5.95,  what  will  1  pound  cost  ? 

43.  A  man  sold  a  cow  for  $72.     If  f  of  this  was  profit, 
what  did  the  cow  cost  him  ? 

44.  If  J  a  pound  of  tea  costs  $.26,  what  will  17  Ib.  cost  ? 

45.  What  number  multiplied  by  72  gives  11232  ? 

46.  Take  .f  of  112  from  f  of  5000. 

47.  At  $4.80  a  dozen,  what  will  9  handkerchiefs  cost  ? 

48.  Reduce  1608  mills  to  higher  denominations. 

49.  How  much  will  a  man  earn  in  a  week  if  he  earns  $2  J 
a  day  ? 

50.  A  farmer  sold  f  of  126  bu.  of  potatoes  at  $.90  a 
bushel.     What  did  he  receive  for  them  ? 

51.  A  house  cost  $4200,  the  barn  ^  as  much.     What 
did  both  cost  ? 

52.  How  many  yards  of  border  will  it  take  for  the  walls 
of  a  room  17  ft.  square  ? 

53.  How  many  pounds  of  butter  at  $.32  a  pound  can  be 
bought  for  $160.64  ? 

54.  A  man  sold  2  bu.  of  peanuts  by  the  half-pint.     How 
many  sales  did  he  make  ? 

55.  262194  -+-  89  =  ? 

56.  From  $200  take  $.082. 

57.  How  long  will  a  tub  of  butter  containing  42  Ib.  last 
a  family,  if  8  oz.  a  day  are  used  ? 


MISCELLANEOUS.  47 

58.  16f  +  18§  +  42J  -  60  =  ? 

59.  A  man  earned  $90  a  month,  and  saved  in  3  months 
$55.20.     How  much  did  he  spend  each  month  ? 

60.  Add  the  odd  numbers  between  10  and  20  and  multi- 
ply the  sum  by  75. 

61.  Find  the  difference  between  Jf  and  £f . 

62.  A  lady  had  3  spools  of  thread  with  50  yd.  on  each 
spool.     She  used  1 J  spools.     How  many  yards  were  left  ? 

63.  At  $4.50  a  ton  what  will  19  tons  of  coal  cost  ? 

64.  Write  the  largest  number  containing  two  groups. 

65.  What  number  must  be  added  to  1083  to  make  4000  ? 

66.  A  barrel  of  cider  at  $.05  a  quart  will  cost  what  ? 

67.  Paid  J  of  $640  for  a  horse,  and  J-  of  what  was  left 
for  a  harness.     What  did  both  cost  ? 

68.  2921  -  189  -  1716  =  ? 

69.  Take  the  sum  of  $4.42  and  $6.20  from  the  differ- 
ence between  $19  and  $2.88. 

70.  If  a  bushel  of  apples  costs  $|,  what  will  21  bu.  cost  ? 

71.  A  boy  had  $J,  $J,  and  3  dimes.     He  spent  J  of  it. 
How  much  had  he  left  ? 

72.  Bought  |  of  a  yard  of  plush  at  $3.52  a  yard,  4  yd. 
of  ribbon  at  $.35  a  yard,  and  had  $2.28  left   in  money. 
How  much  had  I  at  first  ? 

73.  §  of  a  barrel  of  molasses  was  sold  at  $.12  a  quart. 
What  was  received  for  it  ? 

74.  How  many  times  will  a  wheel  9  ft.  in  circumference 
revolve  in  going  15  yards  ?     * 

75.  Find  the  quotient  of  32857  -r-  36. 

76.  A  man  paid  $400  for  a  team  of   horses,  and  sold 
them  at  $187  apiece.     What  did  he  lose  ? 

77.  From  the  sum  of  $27  and  $.27  take  their  difference. 


48 


ARITHMETIC. 


78.  At  f  .06  a  quart  how  many  gallons  of  milk  can  I  get 
for  $1.44  ? 

79.  3  qt.  of  walnuts  cost  $.24.     What  will  3  pk.  cost  ? 

80.  How  many  3-ounce  bags  can  be  filled  from  7|  Ib.  of 
candy  ? 

81.  If  2989  is  taken  from  the  sum  of  1397  and  4209, 
how  much  is  left  ? 


Add: 
82. 


12694 
38563 
72596 
80357 
94261 
80357 
29826 
56837 
43659 
38426 
12564 
37842 
Add:  " 
85.  12964 
83756 
23841 
92084 
64297 
13826 
24927 
12562 
17384 
92644 
75806 
92109 
74318 


83. 


86. 


72846 
38137 
56421 
74363 
82146 
37356 
12945 
73486 
15942 
66735 
70859 
29642 

37642 
92845 
17376 
69524 
83126 
54216 
83709 


52846 
75912 
86402 
91929 
65307 


84. 


87. 


35832 
15737 
26840 
12756 
34265 
19084 
27653 
12642 
98731 
70735 
23853 
73759 

56384 
83792 
47275 
74903 
31296 
96478 
53129 
41379 
83567 
42861 
27272 
93856 
64925 


MISCELLANEOUS.  49 

88.  126430  -r-  54  =  ? 

89.  72426  -T-  87  =  ? 

90.  How  many  2-foot  rules  can  be  cut  from  a  pole  8 
yd.  long  ?  ! 

91.  Paid  |  of  $21  for  a  hat  and  £  of  what  was  left 
for  a  cloak.     What  did  both  cost  ? 

92.  Add  nineteen  dollars  eighteen  cents  ;  two  hundred 
seventy  dollars  three  cents  four  mills ;  sixty-five  dollars ; 
four  dollars  eighteen  cents  nine  mills  ;  eight  hundred  two 
dollars  thirteen  cents  seven  mills. 

93.  How  many  2-quart  pails  could  be  filled   from   a 
hogshead  ? 

94.  If  18  tables  cost  $110.34,  what  is  that  apiece  ? 

95.  Charles  had  J  of  $16  and  spent  |  of  it.     What  did 
he  spend  ? 

96.  A  horse  was  fed  8  qt.  of  oats  a  day  for  12  days  ? 
How  much  was  left  from  11  bu.? 

97.  In  304  gills  how  many  gallons,  etc.? 

98.  3  boys  picked  7  bu.  of  nuts,  and  sold  them  at  $.09 
a  quart.     They  divided  the  money  equally.     What  was  the 
share  of  each  ? 

99.  How  long  will  4  tons  6  cwt.  1  qr.  15  Ib.  of   hay 
last  if  40  Ib.  are  used  daily  ? 

100.  What  will  17f  Ib.  of  crackers  cost  at  $.12  a  pound  ? 

101.  At  $.06  a  yard  what  will  the  cord  around  a  table 
3  ft.  long  and  2  ft.  wide  cost  ? 

102.  How  many  24-inch  steps  would  you  take  in  walking 
32  yd.? 

103.  -4f  A  =  ? 

104.  When  lemons  are  $.24  a  dozen,  what  will  17  baskets, 
each  containing  48  lemons,  cost  ? 


50  ARITHMETIC. 

105.  If  a  steamer  goes  10  miles  an  hour,  how  many  days 
will  it  take  to  go  3120  miles  ? 

106.  A  druggist  sold  alcohol  at  $.10  a  pint.     If  he  paid 
$35  for  a  cask  containing  48  gallons,  what  was  his  gain  ? 

107.  13867  is  the  product  and  49  the  multiplier.     What 
is  the  multiplicand  ? 

108.  How  many  more  pints  are  there  in  18  bu.  than 
in  18  gal.? 

109.  What  number  added  to  23002  will  make  31101  ? 

110.  Find  the  sum  of  $18.36,  $57.043,  $117,  $26.136, 
$.18,  $14,  and  $.009. 

111.  At  $.05  a  quart,  how  many  quarts  of  peanuts  can 
be  bought  for  $15.40  ? 

112.  A  man  left  $7000  to  his  wife  and  three  children. 
The  children  received   $1275  each.     What  did  the  wife 
receive  ? 

113.  79430  is  the  minuend  and  36412  the  subtrahend. 
Find  the  remainder. 

114.  A  lady  started  on  a  journey  with  fifty  dollars.    She 
paid  $16.62  for  railroad  fare,  and  stayed  3  weeks,  paying 
$10.50  a  week  for  board.     How  much  had  she  left? 

115.  A  barrel  of  vinegar  at  $.28  a  gallon  will  cost  what  ? 

116.  If  a  laborer  receives  $.17|  an  hour,  what  will  he 
receive  for  12  hours'  work  ? 

117.  A  farmer  sold  2  bu.  3  pk.  4  qt.  of  clover  seed  at 
$.05  a  quart.     What  did  he  receive  for  it  ? 

118.  A  merchant  gained  $295  by  selling  some  goods  for 
$7640.     What  did  the  goods  cost  him  ? 

119.  If  6  bu.  of  apples  cost  $6.48,  what  will  a  peck  cost  ? 

120.  I  paid  |  of  $.40  for  3  lemons.      How  much  was 
that  apiece  ? 


MISCELLAKEOUS.  51 

121.  From  a  piece  of  cloth  containing  21  yd.,  8§  yd.  were 
cut  at  one  time  and  4i  at  another.     How  many  yards  were 
left? 

122.  4293  -4-  47  =  ? 

123.  If  23  is  the  divisor  and  147  the  quotient,  what  is 
the  dividend  ? 

124.  A  lot  cost  $2600  and  a  house  2£  times  as  much. 
What  did  both  cost  ? 

125.  Bought  9  Ib.  butter  at  $£  a  pound.     How  much 
change  would  I  receive  from  $3  ? 

126.  Add  6134,  74927,  84,  8739,  952,  5734,  and  1286. 

127.  2873  X  94  =  ? 

128.  On  a  card  there  are  4  dozen  buttons.     How  many 
are  there  on  16  cards  ? 

129.  84   sheep  were   sold  for   $300.     If   they  cost    $3 
apiece,  how  much  was  gained  by  the  sale  ? 

130.  28375  ~  15  =  ? 

131.  How  long  would  it  take  a  boy  earning  $1.25  a  day 
to  earn  $120  ? 

132.  Allowing  75  Ib.  to  a  bushel,  how  many  ounces  will 
42  £  bu.  of  corn  weigh  ? 

133.  What  is  the  average  daily  attendance  at  a  school 
if  there  are  916  scholars  present  on  Monday,  938  on  Tues- 
day, 934  on  Wednesday,   927   on  Thursday,   and  915   on 
Friday  ? 

134.  A  milkman  sells  17  customers  each  a  pint  of  milk 
daily,  23  customers  take  a  quart  each,  47  take  2  qt.  each, 
and  8  take  3  qt.  each.     How  much  milk  does  he  sell  in 
a  week  ? 

135.  7  bushels  of   nuts  are  sold   at   $.04   a   half-pint. 
What  did  they  bring  ? 


52  ARITHMETIC. 

136.  A  man  having  5  Ib.  7  oz.  of  candy  sold  3  Ib.  12  oz. 
How  much  had  he  left  ? 

137.  A  man  steps  24  inches  at  each  step.     How  many 
yards  will  he  go  if  he  takes  1279  steps  ? 

138.  What  will  8  months'  rent  amount  to  at  $390  per 
year  ? 

139.  48  Ib.  of  camphor  costing  $.29  a  pound  was  sold  at 
$.03  an  ounce.     How  much  was  gained  ? 

140.  A  man  buys  27  horses  for  $3564,  and  sells  them  at  a 
gain  of  $270.     What  does  he  receive  apiece  for  them  ? 

141.  What  is  the  difference   between   16  X  $3.25   and 
9  x  $4.015  ? 

142.  How  many  pints  in  a  cask  containing  27  gal.  3  qt. 
1  pt.? 

143.  Two  persons  together  earned  $236.     One  had  $32 
more  than  half  of  it.     How  much  had  the  other  ? 

144.  119287  +  18  =  ? 

145.  At  $10  a  week  what  will  a  man's  board  bill  amount 
to  in  17 1  weeks  ? 

146.  What  is  the  distance  in  yards  around  a  table  5  ft. 
long  and  3£  ft.  wide  ?     Illustrate. 

147.  Two  persons  are  1000   miles  apart.      They  travel 
towards  each  other  for  6  days,  one  going  42  miles  a  day  and 
the  other  37.     How  far  apart  are  they  then  ? 

148.  A  farmer  sold  18|  bu.  of  raspberries,  37£  bu.  of 
blackberries,    and   56f    bu.    of   strawberries.     How   many 
bushels  of  berries  did  he  sell  ? 

149.  At  $2.75  a  day,  what  will  it  cost  a  man  to  board 
3  weeks  ? 

150.  A  hogshead  of   maple  sirup  at  $.30  a  quart  will 
cost  what  ? 


CHAPTEE  II. 
FACTORS  AND  MULTIPLES. 

15  is  the  product  of  3  and  5. 

15  is  a  multiple  of  3  and  5. 
3  and  5  are  factors  of  15. 

A  Factor  of  a  number  is  an  integer  that  will  exactly 
divide  it. 

An  Integer  is  a  whole  number. 

3  is  a  factor  of  15,  because  it  is  contained  in  15  without 
a  remainder. 

What  are  the  factors  of  18  ?  of  20  ?  of  24  ?  of  36  ? 

A  number  that  has  no  factors  except  itself  and  1  is  a 
Prime  Number.  17  is  a  prime  number.  Name  several  prime 
numbers. 

A  number  that  has  other  factors  besides  itself  and  1  is  a 
Composite  Number. 

16  is  a  composite  number.     Name  others. 

A  prime  number  used  as  a  factor  is  a  Prime  Factor. 
What  are  the   prime   factors  of  18?    of   20?    of  24? 
of  36? 

Numbers  are  Prime  to  each  other  when  they  have  no 
common  factor  or  divisor.  4  and  9  are  prime  to  each  other, 
but  are  not  prime  numbers.  Name  other  numbers  prime 
to  each  other. 

63 


54  ARITHMETIC. 

A  Multiple  of  a  number  is  a  number  that  exactly  con- 
tains it.     5,  10,  and  15  are  multiples  of  5. 

Give  a  multiple  of  3 ;  of  4  ;  of  6 ;  of  7. 

Give  several  multiples  of  2. 

Give  three  factors  of  18. 

What  number  is  a  factor  of  both  9  and  15  ? 

A  number  that  is  a  factor  of  two  or  more  numbers  is  a 
Common  Divisor  of  them. 

Name  a  common  divisor  of  18  and  24. 

Name  all  the  common  divisors  of  18  and  24. 

What  is  the  greatest  common  divisor  of  18  and  24  ? 

What  is  the  greatest  common  divisor  of  24  and  36  ? 

30  is  a  multiple  of  what  number  ? 

What  number  is  a  multiple  of  both  2  and  5  ? 
.    Give  other  numbers  that  are  multiples  of  2  and  5. 

A  number  that  is  a  multiple  of  two  or  more  numbers  is 
a  Common  Multiple  of  them. 

What  is  a  common  multiple  of  4  and  6  ?  of  3  and  4  ? 
What  is  a  common  divisor  of  24  and  36  ? 
What  is  the  greatest  common  divisor  of : 

1.  20  and  30  4.    10,  15,  and  20 

2.  18  and  27  5.      7,  14,  and  21 

3.  25  and  40  6.    12,  18,  and  24 
Write  the  prime  numbers  from  1  to  25. 

Write  the  composite  numbers  from  1  to  25. 
Name  a  common  multiple  of : 

1.  2  and  7  3.    2  and  6  5.   2,  3,  and  4 

2.  3  and  4  4.    5  and  4  6.    3,  4,  and  5 
Name  three  common  multiples  of  2,  3,  and  4. 


FACTORS   AND   MULTIPLES.  55 

What  is  the  least  common  multiple  of  3,  4,  and  5  ? 

Is  24  a  common  multiple  of  4  and  6  ? 

Give  a  common  multiple  of  4  and  6  that  is  larger  than 
24.  Smaller  than  24. 

What  is  the  least  common  multiple  of  4  and  6  ?  Of 
3  and  6  ? 

What  is  the  least  common  multiple  of  18,  27,  and  30  ? 

Divide  by  any  prime  number  2  )  18,     27,     30 

that  is  exactly  contained  in  any  3  )    9,     27,     15 

two  or   more   of   the   numbers,  3)3,       9,       5 

and   bring  down  the  quotients  1,       3,       5 

and  undivided  numbers.    Divide  2x3x3x3x5  =  270 

again  as  before,  and  so  continue  Ans. 
until  there  is  no  number  that  will  exactly  divide  the  quo- 
tients and  undivided  numbers. 

The  product  of  the  divisors,  quotients,  and  undivided 
numbers  will  be  the  least  common  multiple. 

The  least  common  multiple  of  18,  27,  and  30  is  how 
much  less  than  their  product  ? 

Find  the  least  common  multiple  of : 

1.  5,  16,  and  20  4.    3,  5,  9,  and  10 

2.  9,  14,  and  12  5.    6,  9,  12,  and  18 

3.  4,  12,  and  16  6.    2,  14,  7,  9,  and  3 

7.  From  the  product  of  the  numbers  in  each  of  the  above 
examples,  subtract  their  least  common  multiple. 

Add: 

8.  3264  9.  29832  10.  98462 

987  394  231 

26942  99  9825 

7298  4  259 

369  6943  72491 


56  ARITHMETIC. 

COMMON  FRACTIONS. 

A  common  fraction  is  written  with  two  numbers,  one 
above  the  other,  with  a  line  between  them  :  thus,  f . 

The  number  above  the  line  is  called  the  Numerator.  4  is 
the  numerator. 

The  number  below  the  line  is  called  the  Denominator.  5 
is  the  denominator. 

The  denominator  shows  the  number  of  equal  parts  into 
which  the  unit  is  divided. 

The  numerator  shows  how  many  of  these  equal  parts  are 
taken.  (Illustrate.) 

The  numerator  and  denominator  are  called  the  Terms  of 
a  Fraction. 

A  Proper  Fraction  is  a  fraction  whose  value  is  less  than 
1.  Its  numerator  is  less  than  its  denominator,  as  j. 

An  Improper  Fraction  is  a  fraction  whose  value  is  1  or 
more  than  !«.  Its  numerator  is  equal  to,  or  greater  than,  its 
denominator. 

|  is  an  improper  fraction  because  its  value  is  1.  J  is  an 
improper  fraction  because  its  value  is  more  than  1. 

An  integer  may  be  written  in  fractional  form  by  giving 
it  1  for  a  denominator. 

A  Mixed  Number  is  an  integer  and  fraction  written 
together.  3J  and  oj  are  mixed  numbers. 

Reduction  of  Fractions  is  the  process  of  changing  the 
form  without  changing  the  value. 

Multiplying  both  terms  of  a  fraction  by  the  same  number 
does  not  change  its  value.  (Illustrate.) 

Dividing  both  terms  of  a  fraction  by  the  same  number 
does  not  change  its  value.  (Illustrate.) 

To  reduce  a  fraction  to  higher  terms,  multiply  both  terms 
by  the  same  number. 


REDUCTION    OF    FRACTIONS. 


57 


Eeduce  j  to  60ths,  —  g*  }22  =  g.  (To  find  the  number 
by  which  you  multiply,  divide  the  required  denominator  by 
the  given  denominator.) 

In  the  above  illustration  the  required  denominator,  60,  is 
12  times  the  given  denominator,  5  ;  therefore  the  required 
numerator  must  be  12  times  the  given  numerator. 

Which  is  greater,  f  or  Jf  ?     Why  ? 

Change  the  following  fractions  to  higher  terms  : 

Mental  Work. 
1.    \  to  4ths. 


2.  £  to  lOths. 

3.  f  to  12ths. 


4. 
5. 
6. 

7. 
15. 


to  16ths. 
\  to  48ths. 
to  ? 


8-  f  =  If- 

9.  f  =  if 

10.  f  =  A- 

11-  i? 

12.  J, 


to  12ths. 
to  24ths. 


13.  f  , 

14.  J, 


J  to  28ths. 
,      to  40ths. 


\  to  higher  terms. 

16.  How  many  20ths  in  J 

17.  How  many  66ths  in 

18.  f  equal  how  many  63d  s  ? 

19.  Mary  bought  J  of  a  yard  of  velvet.     How  many 
32ds  of  a  yard  did  she  buy  ? 

20.  Change  ^  to  another  form. 

21.  Change  f  to  a  fraction  having  40  for  a  denominator. 

Written  Work. 

1.  £  to  42ds.  5.  f  |  to  120ths.  9.  f  f  to  500ths. 

2.  f  to  64ths.  6.  ff  to  150ths.  10.  f  J  to  1680ths. 

3.  ^to75ths.  7.  £ftol44ths.  11.  {%  to  522ds. 

4.  iJ  to  96ths.  8.  H  to  128ths.  12.  Jf  f  to  9375ths. 


58  ARITHMETIC. 

13.  {$  to  1330ths.  17.  |,  |,  J,  }i  to  96ths. 

14.  ^  to  43121sts.  18.  f,  3^,  ^  to  250ths. 

15.  }$£  to  1393ds.  19.  ^,  J,  TW  to  lOOOths. 

16.  ,&V  to  988ths.  20.  f,  }|£,  f  *  to  625ths. 

21.  Reduce  |-|  to  a  fraction  having  another  form. 

22.  How  many  328ths  in  £  ? 

23.  There  are  how  many  840ths  in  f,  jj,  £$  ? 

24.  Reduce  ^T  to  higher  terms. 

To  reduce  a  fraction  to  its  lowest  terms : 

Divide  both  terms  by  any  common  factor  ;  divide  the 
result  in  the  same  way,  and  so  continue  until  the  terms  are 
prime  to  each  other.  If  the  terms  are  large,  divide  by 
their  greatest  common  divisor. 

Change  the  following  to  their  lowest  terms : 

Mental  Work. 

1.  £  6.    H  11.    |J 
2-    t                             7.    ft  12.    Jf 

3.  H  8.  ||  13.  f  J 

4.  4  9.  |f  14.  S| 

5.  }£  10.  ft  15.  rffr 
Written  Work. 

I-  *f  8.  ^ft  15.  TVft  22. 

2.  T%  9-  Ml  16-  Hi  23.    J 

3.  H  10.  Jft  17.  m  24. 

4.  H  11.  Jft  18.  ^  25. 

5.  ||  12.  if}  19.  /A  26. 

6-  f*  13.    ^%  20.    Ht  27.    J 

7.  Tftft  I4-    *Wfr  21.    ^ftV  28.    i 

29.  How  many  thirds  in  §|J  ? 

30.  Express  in  simplest  form  98  divided  by  392. 


REDUCTION    OF   FRACTIONS.  59 


31.  Change  -ff/^  to  a  fraction  whose  denominator  is  five. 

32.  Express  in  simplest  form  the  quotient  of  288  divided 
by  504. 

33.  What  is  the  simplest  form  of  |f  f  ? 

To  reduce  a  mixed  number  to  an  improper  fraction. 

5|  apples  equal  how  many  4ths  ? 

In  1  apple  there  are  fou*ths  ?  in  5  apples  there  are  5  X 


4  20       .          20          ,  3 23         __   93 

I     fourths          fourths  ~=    *  ' 


fourths          fourths  '     fourths     '     fourths          fourths 

Rule. 

Multiply  the  integer  by  the  denominator  of  the  fraction ; 
to  the  product  add  the  numerator,  and  write  the  result 
over  the  denominator. 

Reduce  the  following  to  improper  fractions  : 

Mental  Work. 

1.  1J  8.  2f  15.  8ft  22.  12} 

2.  4£  9.  3f  16.  9J  23.  10^ 

3.  3|  10.  4J  17.  10$  24.  llf 

4.  5J  11.  5J  18.  llf  25.  13J 

5.  3J  12.  6f  19.  12J  26.  14^ 

6.  2f  13.  8J  20.  10^  27.  13| 

7.  4J  14.  TfV  21.  11{ 

28.  How  many  eighths  in  13  ?     Change  239  to  the  form 
of  a  fraction. 

29.  How  many  fifths  in  32  ?     Eeduce  25  to  eighths. 

30.  In  15^  weeks  how  many  sevenths  of  a  week  ? 

31.  What  improper  fraction  will  equal  13 J  ? 

Written  Work. 

32.  25£        34.   37^        36.    270§$        38. 

33.  9^        35.    49^         37.    19ft  39. 


60  ARITHMETIC. 


40.    174 

45.    25^ 

50.    29ft 

55.    191^ 

41.    25? 

46.    59^ 

51.    149? 

56.   203^ 

42.    15^ 

47.    67^ 

52.    128f 

57.    98H 

43.   23ft 

48.   89f$ 

53.    137T7s 

58.    87|J 

44.    40J 

49.    131? 

54.   238H 

59.    138W1 

60.  In  237  how  many  ninths  ? 

61.  Reduce  147  to  elevenths. 

62.  How  many  sixteenths  in  250  ? 

63.  Change  128^  to  twenty-sixths. 

64.  In  $730  how  many  nineteenths  of  a  dollar  ? 

65.  Change  297  to  a  fraction  whose  denominator  shall 
be  81. 

66.  Express  in  another  form,  142^. 

67.  There  are  how  many  121  sts  in  401  TJT  ? 

To  reduce  an  improper  fraction  to  an  integer  or  mixed 
number. 

foi^ths  apples  =  how  many  whole  apples  ? 

In  1  apple  there  are  ^^;  in  ^^  apples  there  are  as 
many  apples  as  ^^  is  contained  times  in  ^^-  =  5 
apples. 

23  _  K, 

fourths  ~~        ** 

Rule.  —  Divide  the  numerator  by  the  denominator. 
Change  the  following  to  integers  or  mixed  numbers  : 
Mental  Work. 


1. 

1 

7. 

¥ 

13.    -V3- 

19. 

« 

2. 

i 

8. 

v- 

14.    ff 

20. 

« 

3. 

f 

9. 

¥ 

15.    V 

21. 

f§ 

4 

i 

10. 

V 

16.    lf± 

22. 

ft 

5. 

\a 

11. 

V 

17.    A|* 

23. 

ff 

6. 

i 

12. 

V 

>8.    ft 

24. 

Vi 

REDUCTION   OF   FRACTIONS.  61  * 

25.  In  z^2-  of  a  gallon  how  many  gallons  ? 

26.  In  -Z-J1  of  a  dollar  how  many  dollars  ? 

27.  f  changed  to  sixths  equals  what  mixed  number  ? 

Written  Work. 
1.    JLJI          3.    \^          5.    sff.         7.    Hi*          9-    W 

2-    W          4-    W          6.    W          »•    W          10-    H»a 

11.  *#£  14.    *f$3.  17.    *££•  20.    A|^a. 

12.  affi          15.    *jp  18.    W-  21.    iff^ 

13.  V/  16-    W  19-    -Tff-          22'    *•$%$*• 

23.  How  many  pecks  in  Q-fja.  pecks  ? 

24.  Reduce  £f  f&  to  a  mixed  number. 

25.  In  £f  J^  miles  how  many  miles  ? 

26.  Express  in  another  form,  2^*. 

27.  What  is  the  quotient  of  38540  -r-  197  ? 

28.  Prove  the  above  by  multiplication. 

A  Fractional  Unit  is  one  of  the  equal  parts  of  a  whole 
unit. 

The  fractional  unit  of  £  is  £ ;  of  J  is  J. 

Like  Fractions  are  fractions  that  have  the  same  fractional 
unit;  J,  f,  |,  f. 

Fractions  having  unlike  fractional  units  can  be  changed 
to  those  having  like  fractional  units ;  %,  £,  J  =  T65,  ^,  ^. 

NOTE.  —  Fractions  having  a  common  denominator  are 
like  fractions.  (Illustrate.) 

Fractions  have  a  Common  Denominator  when  their  denom- 
inators are  alike. 

The  common  denominator  of  two  or  more  fractions  is  a 
common  multiple  of  their  denominators. 

The  least  common  denominator  of  two  or  more  fractions 
is  the  least  common  multiple  of  their  denominators. 


62  ARITHMETIC. 

To  reduce  fractions  to  a  common  denominator : 
Reduce  each  of  the  fractions  to  its  lowest  terms.  Mul- 
tiply the  denominators  together  for  a  common  denominator. 
Divide  the  common  denominator  by  the  denominator  of  each 
fraction  and  multiply  both  terms  of  each  fraction  by  the 
quotient.  (Illustrate.) 

Mental  Work. 

Change  the  following  to  fractions  having  a  common 
denominator : 

I-   *,  i  4-  t,  }  7.  i  4,  i 

2.  *,}  6.  },f  8.  f,  i,  } 

3.  J,|  6.  J,i  9.  |,i,i 
Written  Work. 

1-  i,i,»  4.    $,  *,3  7.    |,i,4 

2-  f  J,i  5.    f,f,|  8.    f,J,f 

3-  2,  i,  §  6.    i,|,  |  9.    A»i»* 

NOTE.  —  To  reduce  fractions  to  their  least  common  de- 
nominator, find  the  least  common  multiple  of  the  denomi- 
nators, and  proceed  as  above. 

Change  the  following  to  fractions  having  a  least  common 
denominator : 


Mental  Work. 

1.   i, 

1 

4. 

f  A 

;»J 

7. 

£  *>  T7^ 

2.    §, 

| 

5. 

t.  4> 

T75 

8. 

|,  f,  § 

3-    i, 

| 

6. 

*,  f, 

51! 

9. 

*?l?i 

Written  Work. 

1.   i, 

K'i 

5. 

if, 

1,  A 

9. 

i  t,  f  ,  A 

2-    f, 

t».t 

6. 

i,  f, 

M 

10. 

i  A>  1?  f 

3.    ft, 

A.  4 

7. 

9,  i 

A>  f 

11. 

i?  f  >  3?  T?5 

4.    J, 

1,1 

8. 

i,  ii 

I,  A 

12. 

fc  i  i>  H 

ADDITION   OF   FRACTIONS.  63 

In  how  many  ways  may  fractions  be  reduced?  (Illus- 
trate.) 

ADDITION   OF  FRACTIONS. 
Rule. 

If  the  fractions  are  not  like  fractions,  reduce  them 
to  a  common  denominator  ;  add  their  numerators,  and 
write  the  sum  over  the  common  denominator.  If  neces- 
sary, reduce  the  result  to  lowest  terms.  If  an  improper 
fraction,  reduce  to  an  integer  or  mixed  number. 

To  add  mixed  numbers,  add  the  integers  and  fractions 
separately,  and  unite  the  results.  (Illustrate.) 

Mental  Work. 

Add  the  following  fractions  : 

1.    i,  i  6.  f,  £  11.  2J,4£,  1 

2-    §,*  7.  |,i  12.  i,£,^ 

3.  §,  i  8.  £,  £  13.  H,  2|,  4. 

4.  f,  §  9.  f ,  J,  3  14.  3J,  If,  5 

5.  J,  i  10.  i,  J,  H  15-  »,3*,4 

16.  2i,3j,2i. 

17.  A  man  paid  $|  for  a  book,  $J  for  an  inkstand,  and 
$ J  for  writing  paper.     How  much  did  he  spend  ? 

18.  Mary  has  $§ ;  her  mother  gave  her  $3£.     How  much 
has  she  ? 


Written  Work. 

Addition  : 

1. 

f  A>i 

6.  i,},i,A 

11. 

f, 

f  i  T7T, 

f 

2. 

i>  4>  "i7^ 

7-  *,  A»  ^  i 

12. 

i, 

*,i, 

f 

3. 

§>  f  T7^ 

8-     §>   i?   T^?   A 

13. 

i> 

2»,|, 

6 

4. 

f»i/l 

9-    i,*,*,i 

14. 

i, 

i  2i? 

T?TT 

5.    A»*,i  10.    j,  f,  6,  |  IB.    4|,f,J,/,. 


64  ARITHMETIC. 

16.  t,*,  A>*  21.  6|,  81,  5|,  7| 

17.  6|,  8§,  f ,  i  22.  9J,  5f ,  9,  if 

18.  3,  §,  },  f  23.  j,  I,  f,  f 

19.  I,  4,  §,  If  24.  5J,  7|,  9J,  45 

20.  f,  J,  A>  T8*  25.  14?,  9f ,  10 

26.  A  man  travels  25§  mi.  on  Monday,  37g  mi.  on  Tues- 
day,  on   Wednesday  as  many  miles  as    on  Monday  and 
Tuesday.     How  many  miles  does  he  travel  in  three  days  ? 

27.  A  farmer  has  271  bu.  of  potatoes  in  one  bin,  133f 
bu.  in  another,  47T\  bu.  in  another.     How  many  bushels 
has  he  ? 

28.  Mr.  Brown  has  $130^ ;  his  wife  $25|  more  than  he 
has ;  his  son  $78/?,  and  his  daughter  $5§  more  than  his 
son.     How  much  have  all  ? 

29.  How  many  yards  of  cloth   will  I  have,  if  I  buy 
123J  yd.,  76|  yd.,  and  58§  yd.  ? 

30.  6J  yd.  of  cloth  are  required  for  a  coat,  3|  yd.  for 
trousers,   and  J    yd.   for  a  vest.      How  many  yards   are 
required  ? 

31.  Find  what  your  mother  spends  if  she  pays  $8T\  for 
your  coat,  $9J  for  your  dress,  $4§  for  your  hat,  $2j  for 
your  shoes,  and  $lj  for  your  gloves. 

32.  How  much  land  in  a  farm  of  five  fields  ;  the  first 
contains  26}^  acres,  the  second  50J§  acres,  the  third  41f 
acres,  the  fourth  69|-  acres,  and  the  fifth  52§  acres  ? 

33.  ?  -  28if  =  98§.     ?  -  104T6F  =  99J. 

34.  After  selling  197|  bu.  of  potatoes,  a  farmer  has 
238J  bu.  left.     How  many  bushels  had  he  to  sell  ? 

35.  A  lady  paid  $25^  for  china,  $12|  for  cooking  uten- 
sils, $2|  for  tin-ware,  and  $25i  for  a  stove.    What  was  the 
amount  of  her  bill  ? 


SUBTRACTION   OF   FRACTIONS.  65 

SUBTRACTION   OF  FRACTIONS. 
Rule. 

If  the  fractions  are  not  like  fractions,  reduce  them  to  a 
common  denominator  and  write  the  difference  of  their 
numerators  over  the  common  denominator.  (Illustrate.) 

To  subtract  mixed  numbers,  subtract  integers  and  frac- 
tions separately. 

From  12£ 
Take    _9| 

3J   Ans. 

From  llf   =   lOf     f  cannot  be  subtracted  from  f  ;  take 
Take      5f   =     5f     one  of  the  11  units,  change  to  7ths, 


Oral  Work. 

5f     and  add  the  f  ,  making  lOf  . 

Subtraction  : 

1.    |-i 

5. 

A- 

f 

9. 

7  -    i 

13. 

4 

-14 

2.  f  -  i 

6. 

1- 

f 

10. 

8-    § 

14. 

6* 

-4§ 

3-    1  -i 

7. 

T9<7  - 

J 

11. 

12-  H 

15. 

11 

-8§ 

4.    i-i 

8. 

1|   _ 

3 

12. 

22-44 

16. 

191 

—  9? 

17.  J.  Edmund  Y.  Cooke  of  Cleveland  had  $150,  and 
paid  $21  J  for  printing.     How  much  was  left? 

18.  9  _  ?  =  8J    J  -  ?  =  i     7£  -  ?  =  2J    17  —  ?  =  f 

19.  Thomas  Phillips  bought  a  pony  for  $35.     He  paid 
$14|  cash.     What  does  he  still  owe  ? 

20.  Minuend  75,  subtrahend  24i.     Find  the  difference. 

21.  What  is  the  difference  between  11  and  J  ? 

22.  Given  26f  for  minuend,  19  for  difference  ;  what  is 
the  subtrahend  ? 

23.  8J-  -  7  =  ?     9^T  -  2^  =  ?     12  J  -  |  =  ?     13§  - 


66  ARITHMETIC. 

Written  Work. 

1.  S-J  6.  15    ~2J  11.  H-» 

2.  i-J  7.  8J-4J  12.  |-4 

3.  |  -  i  &.  10          f  13.  ^  -  f 

4.  6     -  J  9.    12J  -5J  14.    H-l 

5.  3f  —  |  10.      8£  —  4J  15.    if  —  £ 

16.  Take  £  from  |.         From  £§  take  ^T. 

17.  From  the  sum  of  $  and  J  take  their  difference. 

18.  What  must  I  add  to  9|  to  make  20 &  ? 

19.  The  sum  of  two  fractions  is  || ;  one  of  the  fractions 
is  £ :  what  is  the  other  ? 

20.  John  had  125J  bu.  of  apples  and  sold  98£  bu.     How 
many  bushels  had  he  left  ? 

21.  91^  -  38$  =  ?     Take  291|  from  378J, 

22.  From  23J  tons  of   coal  13|  tons  were  sold.     How 
many  tons  remained  ? 

23.  A  dressmaker  cut  §  of  a  yard  of  velvet  from  a  piece 
containing  |£  of  a  yard ;   how  many  sixteenths  of  a  yard 
were  left  ? 

DENOMINATE  NUMBERS. 

A  Denomination  is  the  name  of  a  unit  of  weight  or 
measure. 

In  the  number  4  pints,  1  pint  is  the  unit  and  pint  is  the 
denomination. 

A  Denominate  Number  is  a  number  that  has  one  or  more 
denominations ;  as,  6  pecks,  4  qt.  2  pt. 

A  number  having  more  than  one  denomination  is  a 
Compound  Number;  as,  4  qt.  2  pt. 

What  is  a  concrete  number  ? 

Give  several  concrete  numbers  that  are  not  denominate 
numbers. 


LINEAR   MEASURE.  67 

LINEAR    MEASURE. 


12 

inches  (in.) 

1  foot  (ft.) 

3 

feet 

1  yard  (yd.) 

5% 

yards 

1  rod  (rd.) 

40 

rods 

1  furlong  (fur.) 

8 

furlongs 

1  mile  (mi.) 

320 

rods 

1  mile 

5280 

feet 

1  mile 

Oral  Work. 

1.  John  has  a  fish  pole  4  yd.  long.     How  many  inches 
long  is  it  ? 

2.  How  many  rods  in  5  miles  ?     7  miles  ?     1£  miles  ? 

3.  How  many  feet  in  %  mile  ?     3  miles  ?     1£  miles  ? 

4.  Stepping  two  feet  at  a  step,  how  many  steps  will  be 
taken  in  walking  2  miles  ? 

5.  40  rd.  are  what  part  of  a  mile  ? 

6.  2640  ft.  are  what  part  of  a  mile  ? 

Written  Work. 

1.  Eeduce  164808  in.  to  miles,  etc. 

2.  Change  8  mi.  27  rd.  5  yd.  2  ft.  to  inches. 

3.  In  12024  in.  how  many  rods,  etc.  ? 

4.  9  mi.  3  fur.  5  rd.  3  yd.  1  ft.  make  how  many  feet  ? 
6.    The  diameter  of  the  earth  is  7912  miles  ;  how  many 

feet  long  is  it  ? 

6.  The  Atlantic  cable  between  Newfoundland  and  Ire- 
land is  2200  mi.  long.     If  it  cost  10  cents  a  foot,  what  was 
the  whole  cost  ? 

7.  At  2  cents  a  mile,  what  is   the  railroad   fare   from 
Syracuse  to  N.  Y.  City,  the  distance  being  1599840  feet  ? 

8.  Long  Measure  is  used  in  measuring  what  ? 


68  ARITHMETIC. 

Indicated  Work.  —  Division. 

NOTE.  —  Division  is  indicated  by  the  sign  -f-  ,  or  by  writ- 
ing the  dividend  over  the  divisor  with  a  line  between  them  ; 
thus,  16-7-4  may  be  written  *£-. 

1.    8  +  4-j-2  =  ?  2.  (8  +  4)  -f-  2  =  ? 

3.  Which  is  the  dividend   and  which  the    divisor  in 
example  1  ?     In  example  2  ? 

4.  Indicate  the  division  by  the  other  method  in  exam- 
ples 1  and  2. 

Indicate  and  give  results  : 

5.  20  increased  by  the  quotient  of  25  divided  by  5. 

6.  The  sum  of  20  and  25,  divided  by  5. 

7.  The  difference  between  18  and  12,  divided  by  2. 

8.  The  product  of  11  and  6,  divided  by  3. 

9.  150  plus  the  quotient  of  16  divided  by  4. 

10.  If  5  apples  cost  20/,  what  is  the  cost  of  1  apple  ? 
What  is  the  cost  of  7  apples  ? 

11.  Divide  the  product  of  11  and  8  by  4. 

12.  If  5  horses  cost  $750,  what  will  8  horses  cost  ? 

13.  The  product  of  three  factors  is  88.     One  of  the  fac- 
tors is  11.     What  is  the  product  of  the  other  two  ? 

14.  What  number  multiplied  by  16  gives  400  ? 

15.  How  many  yards  of  cloth  at  $5  a  yard  will  pay  for 
15  cords  of  wood  at  $4.00  a  cord  ? 

16.  How  many  eight-quart  cans  will  hold  16  gallons  ? 

17.  Divide  the  product  of  126  and  15  by  189. 

18.  Harry  had  25/,  and  his  uncle  gave  him  50/.     He 
spent  35/  and  divided  the  remainder  equally  among  4  poor 
boys.     How  much  did  each  boy  get  ? 


REVIEW. 

Add  from  right  to  left  and  vertically 

124  +  5789  +  45876  + 

2356  +  18534  +  127302  + 

103497  +  92345  +  246138  + 

876  +  8953  +  68350  + 

91203  +  75638  +   9021  + 

716584  +  36492  +  312325  + 

980705  +  10347  +  253614  + 

875612  +  63826  +  531743  + 

Add  without  copying  : 
1.   3804|  2. 
2756 
31 
945 
5667 
17589^ 


69 


124579 
785673 
103805 
98764 
362958 
873286 
651321 
936432 


1032867 
943758 

3.  437601f 
605712 

4.  308675 
4756 

3854621 

2170£ 

613521 

25043 

7394583 

1438 

6716579 

148394 

29367 

5671432 

76227$ 

832299 

Subtract : 

1.  2478 
954 


7.  12348 
9876 

10.  35214 

9876 


2.  5876 
1259 

5.  1234f 
985$ 


8.  15943J 
798 

11. 


3. 


6. 


24678 
9899 

8765J 
928£ 


9.  1325432 
980993H 


Subtract  without  copying : 

13.   236      14.   3214 
1982  867 


12. 


15. 


12546J 


8231 
923 


70  ARITHMETIC. 

Written  Work. 

1.  Add  forty-three  dollars ;  seven  dollars,  twenty  cents ; 
nineteen  cents ;   twenty-three  dollars,   three    mills ;    forty 
cents,  six  mills  ;  and  eighty-five  cents. 

2.  From  one  hundred  nine  dollars,  subtract  eight  dollars, 
eighty  cents,  eight  mills. 

3.  $840.268  +  $23.01  +  $14296.30  +  $560.005  +  $4.90 
+  $.009  =  ? 

4.  Reduce  $5284.40  to  mills.     $9456.03  to  cents. 

5.  Change  15004  cents  to  dollars.    6524  mills  to  dollars. 

6.  How  many  half-dimes  in  2£  eagles  ? 

7.  Paid  for  building  a  house  $3170.75,   for  painting 
$240.37£,    for    furniture    $1605.40,     for    carpets    $340|. 
How  much  money  did  I  pay  out  ? 

8.  $6.375  X  98  =  ?       $8500  +  125  =  ?        $41.25  ^ 
33  =  ? 

9.  At  £  of  a  dollar  a  pound,  what  cost  376  Ib.  of  maple 
sugar  ? 

10.  ^y  of  a  dollar  equals  how  many  cents  ? 

11.  25  cents  are  what  part  of  a  dollar  ? 

12.  What  will  one  spoon  cost,  if  2  dozen  cost  $47.76  ? 

13.  134£  +  39f  -  35J  =  ?     958J  -  194J  =  ? 

14.  1,244  +  29,567  +  900,580  +  39  +  150  +  6  + 
3,487,639  =  ? 

15.  Multiplicand  246,  the  product  854661 ;  what  is  the 
multiplier  ? 

16.  A  freight  train  ran  399  mi.  one  week  ;  11  times  as 
far  lacking  246  mi.  the  second  week  ;  how  many  miles  did 
it  run  ? 

17.  At  $.87|  each  what  cost  12  doz.  handkerchiefs  ? 

18.  How  many  pints  in  479  barrels  ? 


REVIEW.  71 

19.  A  yoke  of  oxen  cost  $137.     What  will  19  oxen  cost 
at  the  same  rate  ? 

20.  21  yd.  of  muslin  cost  $72.58.     How  much  is  £  yard 
worth  ? 

Oral  Work. 

1.  £  of  32  -  f  x  12  =  ?     |  X  120  +  |  of  56  =  ? 

2.  Divide  the  sum  of  6  and  12  by  their  difference. 

3.  9  X  6  divided  by  the  product  of  2  and  9. 

4.  How  many  times  is  7  +  2  contained  in  60  +  12  ? 

5.  Subtrahend  24,  remainder  49 ;  find  the  minuend. 

6.  Take  the  sum  of  6  and  9  from  their  product. 

7.  What  is  the  product  of  12  and  96  ? 

8.  Divisor   7,  quotient   9,  remainder   5;    what   is    the 
dividend  ? 

9.  How  many  times  is  £  of  16  contained  in  112  ? 

10.  The   product  of   two   numbers    is  210,    one  of   the 
numbers  is  70 ;  find  the  other. 

11.  A  boy  earned  39  cents,  and  his  father  gave  him  21 
cents.     At  15  ct.  each  how  many  doves  can  he  buy  ? 

12.  Take  £  from  20.     From  18  take  17$. 

13.  At  $  J  a  peck,  what  will  2  bu.  of  potatoes  cost  ? 

14.  One  pint  of  molasses  costs  20  ct. ;  what  will  1£  gal. 
cost? 

15.  $18  X  9  =?     22  X  ?  =  154.     640  -*-  ?  =  128. 

16.  How  many  feet  around  a  table  9£  ft.  long  and  3  ft. 
wide? 

17.  Cloves  are  7  ct.  an  ounce.     What  will  4-J-  oz.  cost  ? 

18.  What  are  the  factors  of  26  ?  39  ?  42  ?  63  ? 

19.  Give  4  different  multiples  of  6. 

20.  Give  three  different  factors  of  40. 


72  ARITHMETIC. 

Written  Work. 

1.  How  many  pints,  etc.,  in  1543  gallons  ? 

2.  In  14  gal.  3  qt.  2  gills,  how  many  gills  ? 

3.  Keduce  52  gal.  1  pt.  3  gi.  to  gills. 

4.  Keduce  2024  gi.  to  hogsheads,  etc. 

5.  How  many  quarts  in  4£  hogsheads  ? 

6.  Change  92351  qt.  to  hogsheads,  etc. 

7.  How  many  gills,  etc.,  in  947  gallons  ? 

8.  Keduce  to  gills  and  add  the  results :  14  gal.  1  pt. ; 
18  gal.  3  qt.  1J  pt. 

9.  How  many  mills  in  $6.62£  ?  $.37£  ?  $89£  ? 

10.  1500  cents  equal  how  many  dimes  ? 

11.  2932488  -v-  ?  =  40720.     £  of  1245  -=-  73  =  ? 

12.  I  work  12  weeks  at  $14  a  week ;  how  much  wheat  at 
$1.68  a  bushel  will  pay  my  wages  ?     (Indicate.) 

13.  How  many  hours  in  this  year  ? 

14.  ft  of  319  -  |f  of  96  =  ?     69438  X  131  =  ? 

15.  How  many  times  must  I  fill   a  quart-cup  to  make 
2  barrels  ? 

16.  64  gal.  of  kerosene  oil  cost  $5.12.     What  will  one 
quart  cost  ? 

17.  Change  3  hhd.  to  gills. 

18.  In  1  hhd.  1  bbl.  10  gal.  how  many  quarts  ? 

19.  At  $.06  a  pint,  how  many  gallons  of  molasses  can  be 
bought  for  $7.68  ? 

20.  Add  12l£,  34£,  104^-,  and  7J. 

21.  240  -  103TV  =  ?     512}  -  90^  =  ? 

22.  Give  4  factors  of  340.     Of  198.     Of  160. 

23.  What  is  the  quotient  of  24  times  56  divided  by  7 
times  24  ?     (Indicate.) 


3ITTJ 
REVIEW.  ^^^iUFOjJjiX       73 

Written  Work. 

1.  In  4  bu.  3  pk.  7  qt.  1  pt.  how  many  pints  ? 

2.  In  2099  pt.  how  many  bushels,  etc. 

3.  Change  82  pints  to  bushels,  etc. 

4.  How  many  quarts  in  2  bu.  2  pk.  1  qt.  ? 

5.  32  chaldrons  equal  how  many  pecks  ? 

6.  Reduce  14  bu.  6  qt.  to  pints. 

7.  Reduce  to  pints  and  add  the  results :  7  qt. ;  14£  bu. ; 
2  pk.  ;  138  qt. 

8.  How  many  pints  of  peanuts  can  a  pedler  sell,  if  he 
has  29  bu.  ? 

9.  At  5  ct.  a  half-pint,  how  much  will  he  receive  for  his 
peanuts  ? 

10.  How  many  dollars  in  250  dimes,  16  quarter-dollars, 
and  6  double  eagles  ? 

11.  At  $1.40  a  bushel,  what  cost  2  qt.  of  oats  ? 

12.  Find  the  cost  of  7  bbl.  of  vinegar  at  five  cents  a 
quart. 

13.  Write  in  figures  seventy-four  million,  three  thousand, 
two  hundred  eight,  and  divide  by  59. 

14.  1984  +  936  +  12305  +  894873  +  9973  -  2968  =  ? 

15.  2345  X  239  -4-  121  =  ?     118T7^  +  29|  +  240J  =  ? 

16.  49638  X  498  -  29631  =  ?     345962  -^  196  =  ? 

17.  6,  15,  and  4  are  factors  of  what  number  ? 

18.  From  |  of  720  take  f  of  287. 

19.  Write  1895  in  Roman  Notation. 

20.  Find  3  factors  of  120.     Of  78.     Of  196. 

21.  Dividend  2975,  divisor  85  ;  find  the  other  factor. 

22.  93600  -i-  ?  =  390.     190348  X  107  =  ? 

23.  Find  the  greatest  common  divisor  of  99  and  72. 


74  ARITHMETIC. 

Written  Work. 

1.  Eeduce  2  cwt.  15  Ib.  1  oz.  to  ounces. 

2.  In  2  T.  15  cwt.  40  Ib.  how  many  pounds  ? 

3.  In  41570  Ib.  how  many  tons,  etc.  ? 

4.  In  2936  cwt.  how  many  ounces,  etc.  ? 

5.  How  many  ounces  in  1  T.  12  cwt.  70  Ib.  ? 

6.  Change  3£  tons  to  pounds. 

7.  Reduce  10  Ib.  2  oz.  14  dr.  to  drams. 

8.  How  many  two-ounce  weights  can  be  made  out  of 
100  pounds  of  brass  ? 

9.  What  cost  26  cwt.  of  ham  at  9  ct.  a  pound  ? 

10.  One  horse  eats  6  qt.  of  oats  a  day.     How  long  will 
12  bu.  last  a  span  of  horses  ? 

11.  Oranges  are  worth  3  ct.  each.     How  many  dozen  can 
be  bought  for  $3.60  ? 

12.  648  +  2903  +  18  +  16730  +  24985  +  7039875  + 
39=  ? 

13.  15  men  dig  a  cellar  in  12  days.     How  long  will  it 
take  2  men  ? 

14.  Dividend  346030,  divisor  243.     Find  the  quotient. 

15.  A  railroad  train  travels   at  the  rate  of   a  mile  a 
minute.     How  far  will  it  go  in  a  day  ? 

16.  1649  and  137  are  factors  of  what  number? 

17.  9837650  -r-  293  =  ?     248  X  95  +-  36  =  ? 

18.  At  6J  ct.  a  pound,  what  cost  4£  cwt.  of  sugar  ? 

19.  f  of  168  +  ?  =  2496.     8J  +  lOf  -  1J  =  ? 

20.  9854  x  937  =  ?     298TV  -  39T\  =  ? 

21.  How  many  quarter-acres  in  96  acres  ? 

22.  $748.30  was  spent  for  coal  at  $5.75  a  ton.     How 
many  tons  were  purchased  ? 


REVIEW.  75 

Written  Work. 

1.  In  6  rd.  2  yd.  2  ft.  how  many  feet  ? 

2.  How  many  yards,  etc.,  in  239  inches  ? 

3.  Eeduce  330  ft.  to  rods. 

4.  How  many  inches  in  32  rd.  14£  feet  ? 

5.  Reduce  24960  in.  to  rods,  etc. 

6.  In  4976  fur.  how  many  miles,  etc.  ? 

7.  Change  6|  mi.  to  feet. 

8.  How  many  feet  in  230  rods  ? 

9.  In  4  mi.  3  rd.  1  yd.  2  ft.  how  many  inches  ? 

10.  Eeduce  54950  in.  to  furlongs,  etc. 

11.  Reduce  9860  in.  to  rods,  etc. 

12.  How  many  yards  around  a  school-lot  that  is  12  rd. 
square  ?     (Illustrate.) 

13.  In  176  yd.  how  many  rods  ? 

14.  J  of  a  mile  from  your  house  is  your  school ;  how 
many  feet  is  it  ? 

15.  How  many  rods  in  44  yards  ? 

16.  In  620  rd.  how  many  feet  ? 

17.  10  yd.  of  ribbon  cost  $3.50.     What  will  18  in.  cost  ? 

18.  If  a  foot  of  land  costs  $4.98,  how  much  will  1  rd. 
cost? 

19.  What  will  be  the  cost  of  18  ft.  of  wire  at  $.24  a 
yard? 

20.  How  many  feet  around  a  lot  40  by  38  feet  ? 

21.  1210  -r-  5i  =  ?       315  ^  31£  =  ?      198  -f-  16£  =  ? 
1896  X  29J  =  ? 

22.  316  X  14  x  139  =?      3758930  -r-  127  =  ?      T\  of 
6282  =  ? 

23.  12987  +  10401  +  1605839  +  93  +  70936  =  ? 


76  ARITHMETIC. 

Sight  Work. 

1.  Give  two  factors  of  99.     Of  121.     Of  63.     Of  91. 

2.  What  number  added  to  8  X  4  will  make  60  ? 

3.  Minuend  94,  remainder  39 ;  find  the  subtrahend. 

4.  3  yd.  of  ribbon  cost  72  ct.     How  much  will  one-half 
yard  cost  ? 

5.  7  and  14  are  factors  of  what  number  ? 

6.  Product  84,  multiplier  7  ;  find  the  other  factor. 

7.  Jenny  earned  $.50  on  Monday  and  30  ct.  on  each  of 
the  following  days  in  that  week.    She  had  left  $1.25 ;  how 
much  did  she  spend  ? 

8.  In  $9.50  how  many  mills  ? 

9.  From  36  subtract  §  of  itself. 

10.  8x15-4x10  =  ?     20x3  +  4x6=? 

11.  How  many  times  must  I  take  3£  to  make  7  ? 

12.  9  +  8  +  20  +  17-19  =  ? 

13.  Give  two  equal  factors  of  49. 

14.  How  many  times  £  of  16  is  9  X  8  ? 

15.  James,  William,  and    John  hire  a  boat  for  $3.20. 
James  pays  75  ct.,  William  85  ct.     How  much  does  John 
pay? 

16.  What  will  6  bu.  of  potatoes  cost  at  20  ct.  a  peck  ? 

17.  36  -  (6  +  3)  =  ?     (8 +  6x3) -5-7=?     (30  +  40) 
-7X2=? 

18.  4  qt.  of   oil  can   be  bought  for  32  ct.     How  many 
quarts  can  I  buy  for  $1.60  ? 

19.  How  many  quarts,  etc.  in  39  pecks  ? 

20.  2£  +  3J  -  H  =  ?     ^f10-  =  ?     241f  =  ? 

21.  126  X  7  =  ?     980  X  11  =  ?     1908  -r- 12  =  ? 

22.  139-18^  =  ?     27£ -6|=?     ^of!56=? 


DRILL   EXERCISES. 


77 


Rapid  Mental  Work. 

Add: 


1. 

4  + 

i 

5 

.  4  +  * 

12 

+  A 

13 

.  4 

+  w 

2. 

i  +  4      6.   J  +  A 

10.   1 

-f-T1! 

14 

•  4 

+  TV 

3. 

4  + 

| 

7. 

4  +  4 

11.  J. 

4-iV 

15 

•  4 

+  4 

4. 

4  + 

i 

8, 

•  T*r  +  lv 

12.  A 

-l-i 

16 

•  \ 

+  A 

Subtract  : 

17. 

i- 

| 

21, 

.  *-4 

25.  J  - 

-iV 

29 

-  A 

IT 

18. 

J- 

4 

22, 

•  *,-* 

26.  \  - 

-A 

30 

•  4 

-TV 

19. 

i  - 

4 

23, 

*-iV 

27.  J-  - 

-A 

31 

•  4 

-TV 

20. 

i  — 

i 

24, 

4-4 

28.  J  - 

-Vr 

32 

•  4 

-TV 

Written 

Work, 

33. 

121 

X 

21 

48. 

7822 

X 

11 

34. 

178 

X 

51 

49. 

8739 

X 

12 

35. 

1234 

X 

31 

50. 

9876 

X 

15 

36. 

1579 

X 

61 

51. 

2347 

X 

13 

37. 

2345 

X 

41 

52. 

7823 

X 

16 

38. 

298 

X 

71 

53. 

1578 

X 

14 

39. 

304 

X 

91 

54. 

6352 

X 

17 

40. 

1235 

X 

101 

55. 

2796 

X 

19 

41. 

2479 

X 

121 

56. 

3498 

X 

18 

42. 

1783 

X 

111 

57. 

8793 

X 

102 

43. 

243 

X 

81 

58. 

25796 

X 

103 

44. 

225 

X 

131 

59. 

25879 

X 

107 

45. 

1256 

X 

141 

60. 

12576 

X 

104 

46. 

897 

X 

151 

61.  283546 

X 

109 

47. 

976 

X 

161 

62. 

85063 

X 

110 

63.  8793 

+  7632  +  98764  + 

79321 

. 

64.  3579 

+  25680  + 

543872 

+  895470. 

78  ARITHMETIC. 

Written  Work. 

1.  In  4  wk.  1  da.  2  h.  how  many  minutes  ? 

2.  Change  305840  sec.  to  years,  etc. 

3.  If  a  clock  loses  4  sec.  an  hour,  how  much  time  will 
it  lose  in  3  days  ? 

4.  How  much  time  will  a  person  waste  in  a  year,  if  he 
wastes  30  min.  every  day  ? 

5.  If    I  cut  30  oranges  into  sixths,  how  many  pieces 
have  I  ? 

6.  If  10  yd.  of  cloth  cost  $35,  what  will  3  yards  cost  ? 

7.  If  £  of  a  ton  of  coal  costs  $2.00,  what  will  5  tons 
cost  ? 

8.  A  man  bought  a  carriage  for  $54  ;   spent  $20  for 
repairs,  then  sold  it  so  as  to  gain  $19.00.     What  did  he 
receive  ? 

9.  Divide  the  product  of   12,  23,  14,  and  13   by  the 
difference  between  160  and  39. 

10.  A  tree  68  ft.  high  was  broken  off  by  the  wind ;  the 
broken   part  was   49    ft.     How  high  was   the   remaining 
portion  ? 

11.  How  many  gallons,  etc.  in  2495  pints  ? 

12.  In  470  qt.  how  many  bushels,  etc.  ? 

13.  How  many  feet  in  324  rods  ? 

14.  If  you  go  to  bed  at  half-past  seven,  and  rise  at  six 
o'clock,  how  many  hours  do  you  sleep  ? 

15.  Bought  a  bushel  of  nuts  at  $2  and  sold  them  at 
5  ct.  a  pint.     What  did  I  gain  ? 

16.  How  many  feet  in  18  rods  ? 

17.  In  840  da.  how  many  weeks  ? 

18.  What  will  12  fans  cost  if  seven  cost  $27.86  ? 


INDICATED   WORK.  79 

* 

INDICATED  WORK. 

Cancellation. 

Indicate  the  division  of  : 

1.  6  apples  by  3  apples. 

2.  6  times  1  apple  by  3  times  1  apple. 

3.  8  twos  by  4  twos. 

4.  8  times  2  by  4  times  2. 

5.  Twenty-four  7's  by  six  7's. 

6.  24  times  7  by  6  times  7. 

7.  18  x  6  by  9  x  6.          8.    40  X  11  by  8  X  11. 
When  the  same  factor  appears  in  both  dividend  and 

divisor,  the  quotient  will  be  the  same  if  that  factor  is  cut 
out,  or  cancelled,  from  both. 

9.    How  many  times  is  6  X  5  contained  in  17  X  5  ? 
SOLUTION.  —  First  indicate  the  division,  thus:     17  X  5 
As  the  factor  5  appears  in  both   dividend   and       6x5 
divisor,     it    should    be     cut     out,     or    cancelled,    thus  : 


10.  Prove  this  work  by  the  long  method. 

11.  Change  examples  2,  4,  6,  and  8  to  read  like  example 
9,  and  find  results  by  cancellation. 

12.  Divide  3x5x7x2  by  3  X  5  X  11. 

What  factors  appear  in  both  dividend  and  divisor  ? 
After  these  are  cancelled,  what  is  left  in  the  dividend  ?  In 
the  divisor  ? 

13.  Divide  the  product  of  5  times  7  times   17  by  the 
product  of  11  times  5  times  7. 

14.  Divide  6  x  11  X  16  by  6  X  11  X  13. 

15.  Divide  46  X  58  X  90  by  46  x  58  X  90. 

16.  Divide  24  X  36  X  17  by  24  x  36  X  13. 


80  ARITHMETIC. 

• 

Written  Work. 

1.  At  the  rate  of  $.36  a  dozen,  what  will  11  lemons 
cost? 

2.  How  many  years  in  19  centuries 

3.  At  J  of  a  dollar  a  pound,  what  costs  a  box  of  tea 
weighing  35  pounds  ? 

4.  How  many  inches  in  24  yd.  ? 

5.  960345  -r-  296  =  ?     649638  X  498  -  38731  =  ? 

6.  3406  X  107  -*-  368  =  ?     9085763  ^  193  =  ? 

7.  A  man  has  a  lot  24  rd.  long  and  20  rd.  wide.     How 
many  rods  around  £  of  it,  if  divided  by  a  fence  parallel  to 
the  long  sides  ?     How  many  rods  around  £  of   it,  when 
divided  by  a  fence  parallel  with  the  short  sides  ? 

NOTE.  —  Pupils  should  draw  diagrams  before  solving. 

8.  Bought  6  bu.  of  corn  for  $4.20 ;  sold  5  bu.  for  $4.20. 
How  much  did  I  gain  on  what  I  sold  ? 

9.  A  merchant,  by  selling  tea  at  $.50  a  pound,  loses 
$.225.     What  did  it  cost  him  ? 

10.  A  building  worth  $25675  is  insured  for  J  of  its 
value.     For  what  amount  is  it  insured  ? 

11.  A  wheel  3  ft.  6  in.  in  circumference  will  turn  how 
many  times  in  going  a  mile  ? 

12.  Multiply  together  the  even  numbers  between  3  and 
41.     The  prime  numbers. 

13.  Find  the  product  of  12547  and  546.     Express  the 
product  in  words. 

14.  An  acre  of  land  produces  25  bu.  of  oats.    How  many 
quarts  will  18  acres  produce  ? 

15.  $6903.07  +  $9564.305  +  $12018  +  $96138.42  + 
$.03  =  ? 

16.  (24J  +  18*)  -  (19J  +  14*)  =  ?     68       -  15    =  ? 


MISCELLANEOUS.  81 

Written  Work. 

1.  Write  a  number  of  three  periods. 

2.  Divide  the  number  in  Ex.  1  by  79. 

3.  1246  -f  329073  +  907  +  3647809  +  7069875  =  ? 

4.  |  of  960  -  ft  of  288  =  ?    96542  x  937  =  ? 

5.  At  $.05  a  half-pint  what  will  a  barrel  of  oil  cost  ? 

6.  Product   $24875,  multiplier  95  ;    find  the  multipli- 
cand. 

7.  Divide   the   sum  of   194703    and   191893   by  their 
difference. 

8.  695430  -f-  127  =  ?      1073825  -f-  201  =  ?      372984 
-^  37  =  ? 

9.  124J  +  29|  -  37J  =  ?     16J  -  4J  +  391*  =  ? 

10.  How  many  quarter-dollars  in  $50  ? 

11.  Paid  $16£  for  coal,  $12  J  for  wood ;  how  much  change 
did  I  receive  from  a  fifty-dollar  bill  ? 

12.  Take  29  X  942  from  65  X  875.     24893  X  297  =  ? 

13.  Subtrahend  98560,  remainder  340875 ;  find  the  min- 
uend. 

14.  The  sum  of  six  numbers  is  9,580,765;    five  of  the 
numbers    are   2,480;    396,407;    24,999;    38,950;    and   37. 
What  is  the  sixth? 

15.  $26,403  -  $9,544.307  =  ?     /5  of  32,240  x  79  =  ? 

16.  How  many  yards  of  border  shall  I  need  for  a  room 
16£  ft.  long  and  14£  ft.  wide  ? 

17.  How  much  will  the  above  border  cost  at  $.35  a  yard  ? 

18.  What  is  the  greatest  common  divisor  of  35  and  63  ? 

19.  At  75  ct.  a  bushel,  how  many  bushels  of  apples  will 
pay  for  8  chairs  valued  at  $1.25  each  ?     (Indicate.) 

20.  780932  -T-  113  =  ?     1532467  -5-  76  =  ?     1038916  -*- 
103  =  ? 


82  ARITHMETIC. 

Sight  Work. 

1.  10  x  10  —  35  -5-  7  =  ?     6x4  +  50-f-5  =  ?    8 
X  9  X  2  -  50  =  ? 

2.  How  many  half-pints  in  4  bushels  ? 

3.  What  will  1£  gal.  of  oysters  cost  at  $.20  a  pint  ? 

4.  At  88  ct.  a  bushel,  what  will  -J-  pk.  of  peas  cost  ? 
6.    How  many  days  in  this  and  next  month  ? 

6.  A  boy  sells  8  qt.  of  peanuts  in  a  day.     How  many 
bushels  will  he  sell  in  12  days  ? 

7.  How  many  feet  in  156  inches  ? 

8.  In  $25  how  many  5-cent  pieces  ? 

9.  5  men  can  build  a  cellar  wall  in  16  da.     How  long 
will  it  take  10  men  ? 

10.  If  2  apples  cost  3  ct.,  how  many  can  you  buy  for 
30  cents  ? 

11.  What  will  8  bananas  cost  if  2  dozen  cost  48  cents  ? 

12.  What  is  my  laundry-bill  if  I  have  18  pieces  at  $.60 
a  dozen  ? 

13.  Give  four  factors  of  120. 

14.  $5.60  x  10  -*-  40  =  ?     j  +  ?  =  f  f .      4*  -  ?  =  1J. 

15.  72  gal.  of  milk  will  fill  how  many  quart-cans  ? 

16.  If  you  have  fifteen  minutes  recess  daily,  how  many 
hours  will  you  have  in  2  weeks  ? 

17.  Change  5  dimes,  10  half-dimes,  and  J  of  a  dollar  to 
cents. 

18.  Find  two  factors  of  121.     Of  143.     Of  49. 

19.  WThat  is  the  sum  of  the  numbers  in  the  above  example  ? 

20.  Dividend  14  X  9,  divisor  7  ;  what  is  the  quotient  ? 

21.  Find  the  greatest  common  divisor  of  21  and  28. 

22.  6  X  3  -  72  -f-  12  =  ?     18  +  40  +  39  -  14  =  ? 


INDICATED    WORK,  83 

INDICATED   WORK. 

Cancellation. 

1.  Divide  8  X  18  x  15  x  7  by  4  x  6  x  11  X  9. 
225  Since  4  and  6  are  factors  of  8  and 
$  X  Iff  X  Iff  X  7     13  respectively,  they  may  be  cancelled 
£  X    0  X  11  X  £      from  both  dividend  and  divisor,  leaving 

*  the  factors  2  and  3  in  the  dividend. 
Cancelling  the  factor  3  from  9  in  the  divisor  and  15  in  the 
dividend,  leaves  3  in  the  divisor  and  5  in  the  dividend. 
Cancel  the  factor  3  again  from  both  dividend  and  divisor. 
The  product  of  the  uncancelled  factors  in  the  dividend  is 
70,  and  in  the  divisor  is  11.  70  -r- 11  =  6T\. 

2.  Divide  36  X  27  X  49  X  38  X  50  by  70  x  18  X  15. 
First  find  result  by  long  method,  then  by  cancellation, 

and  see  how  much  time  is  gained  by  cancelling. 

3.  Divide  the  product  of  28  X  38  X  48  by  the  product 
of  14  x  19  X  24  x  2  x2. 

4.  (26  X  5  x  54)  -5-  (13  X  5  X  6)  =  ? 

5.  What  is  the  quotient  of  36  X  48  X  16  divided  by 
27  X  24  x  8  ? 

Indicate  and  find  result  by  cancellation. 

6.  How  many  bushels  of  apples  at  50/  a  bushel  must 
be  given  for  15  Ib.  of  tea  at  40/  a  pound  ? 

7.  If  5  horses  cost  $600,  what  will  8  horses  cost  ? 

8.  How  many  yards  of  cloth  can  be  bought  for  $40, 
when  60  yd.  cost  $120  ? 

Add  from  right  to  left : 

9.  3694  +  8976  +  38421  +  25982  =  ? 
Multiply  without  copying : 

10.  5894  X  9  =  ?     68463  X  7.     3862  x  8. 
Divide  by  short  division : 

11.  3694  by  6.     7852  by  10.     6985  by  9. 


84 


ARITHMETIC. 


Add: 

1.  450135  +  69089  = 
680506  +  35025  = 

66077  +  3498  = 
940461  +  38690  = 

76274  +  85176  = 

Subtract : 

3.  133-  75 

4.  140-  84 
6.    122-  73 

6.  112-     46 

7.  740-280 

8.  500-219 
Multiply : 

21.  149  X    23 

22.  147  X  122 

23.  146  X  147 

24.  134  X  125 

25.  147  X  431 

26.  143  X  332 
Divide  : 

39.  1392  -i-24 

40.  2084  -r-  26 

41.  1864-^29 

42.  1272  -f-  27 

43.  5176 -T- 19 


2.   85785  +  643066 

48740  +  678459 

5624  +  575535 

56025  +  390154 

315270  +  421280 


9.  810-560 

10.  121  -    65 

11.  146-    61 

12.  134-     78 

13.  269-134 

14.  620-370 

27.  238  X  235 

28.  249  X  225 

29.  248  X  238 

30.  225  X  237 

31.  235  X  246 

32.  227  X  235 


44.  21515 -f- 97 

45.  10414-^84 

46.  9170  -T-  75 

47.  6101  -^  51 

48.  18017^36 
Perform  the  indicated  operations : 

54.  §  +£  57.    21J  —  ' 

55.  |  +  |  58.    19J  — 

56.  J  +  |  59.    14|  + 


15.  376  - 

16.  437  - 

17.  658  - 

18.  1124- 

19.  1112  - 

20.  1237- 

33.  1827  X 

34.  7520  x 

35.  8984  X 

36.  6575  x 

37.  3825  X 

38.  2765  X 


49. 
50. 
51. 


43379 
75405 
210562 

52.  1695832 

53.  2601879 


-  16|  + 


293 
247 
312 
189 
156 
169 

309 
207 
329 
535 
491 
513 

-f-  123 
-f-  345 
-^  624 
-^-3024 
-^4068 


MISCELLANEOUS.  85 

1.  Add  twenty-five  million,  five  hundred  seventy-eight 
thousand,  three  hundred  seven  ;  forty  thousand,  nine  ;  two 
hundred  seventy-six;  one  million,  two  thousand,  and  one. 

2.  The  product  is  $713184,   the  multiplicand  $2346. 
What  is  the  other  term  ? 

3.  234  x  146  -  197  X  95  =  ?     897038  -f-  123  =  ? 

4.  How  is  the  dividend  obtained  when  the  quotient, 
divisor,  and  remainder  are  given  ?     (Illustrate.) 

5.  Dividend   36  X  914  ;    divisor    6  X  56.       Find   the 
quotient. 

6.  Reduce  to  other  forms  y^s ;  *?^  ;  248f§;   Jf  ;   afji. 

7.  18J  +  24ft  -  ?  =  24  &•     16031  x  907  =  ?    . 

8.  197  and  128  are  the  factors  of  what  number  ? 

9.  Multiply  987  by  itself. 

10.  $78563  -  $1735.841  =  how  much  ? 

11.  A  purse  worth%$3  contains  the  largest  9  U.  S.  coins. 
What  are  purse  and  contents  worth  ? 

12.  What   number  added   to   17  x  39    will   make   408 
X  706? 

13.  Divide  34768  by  16,  and  the  quotient  by  13. 

14.  Bought  50   Ib.   sugar  at  $.05£  a  pound,  giving  in 
return  6£  doz.  eggs  at  $.40  a  dozen,  and  the  remainder  in 
cash  ?     How  much  was  the  cash  ? 

15.  Write  two  numbers,  one  odd  and  the  other  even,  that 
are  divisible  by  99.  , 

Add: 

16.   51463  17.  21784  18.  245678 

172903  158304  31235 

278631  197428  8765 

3895746  160895  432 

6387595  598606  9872 


86  ARITHMETIC. 

1.  How  many  days  in  the  winter  months  ? 

2.  6  X  998  -r-  39  =  ?     648751032  +•  297  =  ? 

3.  In  735270  in.,  how  many  miles,  etc.  ? 

4.  A  lady  uses  5  yd.  of  ribbon  for  rosettes.    If  she  uses 
1 8  in.  for  each  rosette,  how  many  will  she  have  ? 

5.  1613  to  27ths.     129J  +  38ft  +  194  =  ? 

6.  248  fr  to  66ths.     J j-J  to  20ths. 

7.  9437  +  207839  +  51697  +  666098  +  9017832  + 
60012  =  ? 

8.  67048164  -5-  ?  =  9876.     24  x  ?  =  95160. 

9.  5148  is  a  multiple  of  two  numbers.     66  is  one,  what 
is  the  other  ? 

10.  How  many  miles  in  1943040  feet  ? 

11.  1600060  -5-  (11  x  2  x  7)  =  ?     6816600  -g-  (3  x  7 
X  5)  =  ? 

12.  7150990  -f-  77  =  ?     2  x  4595200  -4-  ?  =  71800. 

13.  The  school  lot  is  12  rd.  front ;  how  many  feet  is  it  ? 

14.  How  many  half-pints  in  1^  barrels  ? 

15.  What  is  the  total  weight  of  6  bales  of  hay  weighing 
8|  cwt.,  5ft  cwt.,  4£  cwt.,  7J  cwt.,  6£J  cwt.,  and  5£  cwt.  ? 

16.  What  is  the  difference  between  ^  of  880  and  J  of 
9680? 

17.  Quotient  560,  dividend  218400.     Find  the  divisor. 

18.  At  $.06£  a  pint,  how  much  do  I  receive  for  8  bu. 
6  quarts  of  berries  ? 

19.  What  will   13    Ib.  of  spice   cost   at  2£  ct.  a   half- 
ounce  ? 

20.  5}  +  9f  —  8|  =  ?  23.    17J  +  ?  = 

21.  89 J  -  78f  +  39  =  ?         24.    ?  +  29}  = 

22.  18T\  +  39  -  10J  =  ?       25.    249T^  -  12      =  ? 


MISCELLANEOUS.  87 

Denominate  Numbers. 
Add: 

1.  3  mi.  7  fur.  5  rd.  5.    3  gal.  2  qt.  1  pt.  2  gi. 
5  mi.  1  fur.  6  rd.  7  gal.  5  qt.  2  pt.  3  gi. 

2.  3  yd.  2  ft.     5  in.  6.    3  da.  12  hr.  45  min. 
1  yd.  1  ft.  10  in.  9  da.  16  hr.  40  min. 

3.  14  Ib.    7  oz.  7.      3  rd.  1  yd.  1  ft.  6  in. 

7  Ib.  10  oz.  5  rd.  1  yd.  2  ft.  8  in. 

45  Ib.  11  oz.  17  rd.  2  yd.  1  ft.  7  in. 

4.  3  pk.  5  qt.  1  pt.  8.    7  cwt.  30  Ib.     8  oz. 

1  pk.  7  qt.  1  pt.  9  cwt.  50  Ib.     9  oz. 
5  pk.  4  qt.                                3  cwt.  40  Ib.  10  oz. 

Subtract : 

1.  5  wk.  6  da.  19  hr.  6.    125  cwt.  8  qr.  5  Ib. 

2  wk.  3  da.  17  hr.  85  cwt.  9  qr.  3  Ib. 

2.  29  gal.  3  qt.  1  pt.  7.    7  mi.  30  rd.  9  yd. 
14  gal.  2  qt.  1  pt.  4  mi.  17  rd.  8  yd. 

3.  9  bu.  6  pk.  7  qt.  8.    35  Ib.  10  oz.  5  dr. 
5  bu.  7  pk.  3  qt.  IT  Ib.  12  oz.  8  dr. 

4.  7  T.  3  cwt.  23  Ib.  9.   25  bu.  3  pk. 

3  T.  5  cwt.  16  Ib.  15  bu.  5  pk.  1  pt. 

5.  15  yd.  2  ft.  7  in.  10.    8  bbl.  31  gal.  2  qt. 

5  yd.  6  ft.  2  in.  7  bbl.     9  gal.  3  qt. 

11.  What  is  a  denomination  ? 

12.  What  is  a  denominate  number  ? 


88  ARITHMETIC. 

Sight  Work. 

Reduce  to  whole  or  mixed  numbers : 

i-  ¥>  ¥>  1F>  ai*>  f  J,  W>  W»  W>  ^F- 

2.  £  gallon  equals  how  many  pints  ? 

3.  How  many  inches  in  £  f t.  +  J  ft.  +  }  foot  ? 
4-    A  =  i,  =  A,  =  TV     »*  +  3J  +  4£  =  ? 

5.  I  bought  J  of  a  yard  of  ribbon  for  1  hat,  and  f  for 
another.     How  many  inches  of  ribbon  did  I  buy  ? 

6.  Sold  §  of  a  pound  of  coffee  to  one  customer,  and  j  of 
a  pound  to  another.     How  much  was  sold  ? 

7.  What  part  of  an  hour  is  50  minutes  ? 

8.  121  is  a  multiple  of  what  two  numbers  ? 

9.  Change  $24.38  to  cents. 

10.  In  25  dimes  and  4  mills,  how  many  mills  ? 

11.  $8.75  equals  how  many  5-cent  pieces  ? 

12.  In  4£  bu.  how  many  pints  ? 

13.  Sold  8  bu.  of  nuts  at  2  ct.  a  pint.    How  much  money 
did  I  receive  ? 

14.  At  6  ct.  a  pint,  how  many  gallons  of  molasses  can  be 
bought  for  $3.84  ? 

15.  What  will  8  erasers  cost  at  $1.56  a  dozen  ? 

16.  If  one  clothespin  cost  %  cent,  what  will  3  doz.  cost  ? 

17.  8  X  9  -  2  X  6  =?     295  X  7  =?     9588  --  12  =? 

18.  What  will  one-half  bushel  of  sweet  potatoes  cost  at 
$.37£  a  peck  ? 

19.  At  15  ct.  a  quart,  what  will  12  qt.  of  strawberries 
cost? 

20.  How  many  times  must  I  take  4£  to  make  18  ? 

21.  6J  +  5§  =  ?     19|  X  12  =  ?     30J  -  10£  =  ? 

22.  849  +  3  +  7  +  5  + 10 +  12 +  7  +  4  + 11  =  ? 


MISCELLANEOUS.  89 

Written  Work. 

1.  Mary  had  $ 39J ;  she  spent  $27f .     How  much  was 
left? 

2.  Paid  $190f  on  a  bill,  and  I  still  owe  $105f .     What 
was  the  entire  bill  ? 

3.  Eeduce  24  chal.  2  bu.  2£  pk.  7f  qt.  to  pints. 

4.  In  528,  how  many  ninths  ? 

5.  Express  in  figures  MDCCCLXXXIY. 

6.  1235407  -  (9456  +  8578)  X  79  =  ? 

7.  How  many  weights,  weighing  a  quarter  of  a  pound 
each,  can  be  made  from  128  Ib.  of  iron  ? 

8.  7056   pk.   will  fill    how  many   barrels,   each   barrel 
holding  3  bushels  ? 

9.  How  many  3-inch  pieces  can  be  cut  from  48  ft.  of  wire  ? 

10.  Write  4956  in  Roman  notation. 

11.  Express  in  its  simplest  form  the  quotient  of  1340  -j- 
2660. 

12.  J  of   a  hogshead  of   oil   was  sold.     What   did  the 
remainder  bring  at  7  ct.  a  quart  ? 

13.  Of  what  number  are  5,  7,  3,  and  9  factors  ? 

14.  Eeduce  99  mi.  to  feet. 

15.  Express  in  other  forms  17}§  ;  *f jj*;  Tg|jj ;  293^. 

16.  125  x  5  -  ?  =  100.     295873  -5-  73  =  ? 

17.  How  many  quart-boxes  will  hold  79  bu.  1  pk.  3  qt. 
of  grapes  ? 

18.  How  many  times  can  you  fill  a  bushel  measure  from 
15872  pints  of  beans  ? 

19.  36}  +  19J  -  27^  =  ?     20^  +  29  -  16J  =  ? 

20.  107^  +  16?  -  29  =  ?     92  -  16|  +  3|  =  ? 

21.  A  half-pint  bottle  can  be  filled  how  many  times  from 
724  gal.  2  quarts  ? 


90 

ARITHMETIC. 

Add: 

1.  71£ 

2.   26^ 

3.  132$ 

171J 

35J 

•   607J 

37| 

59^ 

irif 

i 

14 

182£ 

4.  119g 

6.  195 

6.  124J 

108| 

47J 

156J 

QO  1 

*J£i£ 

91ii 

132| 

307 

198 

39| 

7. 

8.  j  +  43g  +  72| 

9.  66$  +  5J  +  89|  +  37| 

10.  71J  +  32|  +  83J  + 

11.  94}  +  19J  +  67|  + 

12.  96/j  +  42^  +  71  §  +  66 J 

13.  49J  +  23i  +  81J  +  16^ 

14.  8g  +  16i  +  34|  +  301 J 

15.  14}  +  19$  +  115J  +  334| 

16.  93J  +  27^  +  103J  +  1215 

17.  905|  + 814  +  73|  + 39| 

18.  2307|  +  121  %  +  114*  +  79 

19.  13J  +  14/j  +  15|  +  16J 

20.  19i  +  18ft  +  17}  +  18| 

21.  118J +  147J +  132|  + 60ft 

22.  90J  +  701}  +  |  +  27 

23.  10-^ 

24.  113}  +  99  +  26£  + 

25.  460  +  909ft  +  54f  +  28}. 


MISCELLANEOUS.  91 

Written  Work. 

1.  A  thermometer  showed  at  noon  74^  degrees  above 
zero.    At  6  o'clock  P.M.  it  showed  66|  degrees.    How  much 
had  the  mercury  fallen  ? 

2.  A  grocer  buys  12  bu.  of  sweet  potatoes  for  $14.    He 
sells  them  at  50  ct.  a  peck.     Does  he  gain  or  lose,  and  how 
much  ? 

3.  Skates   bought  for   $3£    were   sold    for   $2£.     How 
much  was  lost  ? 

4.  Gave  £  of  $1500  to  my  brother  and  ^  to  my  sister. 
How  much  have  I  left  ? 

5.  8|  +  11?  -  6f  =  ?     94J  -  30f  +  19i  =  ? 

6.  #16|  +  $90^  +  $120  +  $345£  +  $98§  =  ? 

7.  $7012.06  +  $8072.02£  +  $7865  =  ? 

8.  A  man  carries  3  tons  of  coal  in  a  basket  holding 
50  Ib.     How  many  times  does  he  fill  the  basket  ? 

9.  From  a  barrel  of   oil  7J   gal.  leaked.      How  many 
quarts  remained  ? 

10.  If  2  bu.  of  nuts  cost  $6.40,  what  costs  a  half-pint  ? 

11.  }  of  1099  -  191  =  ?     ^  of  2232  x  903  =  ? 

12.  How  many  hours  in  one  half-day  ? 

13.  In  the  winter  season  how  many  days  ? 

14.  Reduce  24  rd.  3|  ft.  to  inches. 

15.  Bought  175^  bu.  of  potatoes  at  one  time,  97£  bu.  at 
another,  then  sold  89|£  bushels.     How  many  bushels  were 
left? 

16.  Tom  steps  2  ft.  at  each  step.     How  many  rods  will 
he  travel  in  walking  99  steps  ? 

17.  How  many  half-yard  pieces  can  be  cut  from  114  ft 
of  ribbon  ? 

18.  27£  +  39£  -  13J  =  ?     640-301^  +  69!  =  ? 


92  ARITHMETIC. 

Written  Work. 

1.  William  J.  Fitzgerald  made  $75 J  on  Monday;    on 
Tuesday  $17§  more  than  on  Monday ;  on  Wednesday  as 
much  as  on  Monday  and  Tuesday  together.     How  much 
did  he  make  in  all  ? 

2.  4832  X  673  +  ft  of  3175  =  ? 

3.  587654  +  345  =  ?     1956  X  49  +  36  =  ? 

4.  A  merchant  buys  30^  Ib.  of  tea  at  one  time,  25%  Ib. 
at  another,  and  39J  Ib.  at  another.    He  sells  17J  Ib.  to  one 
customer,  and  25J  Ib.  to  another.     What  is  left  ? 

5.  A  man  earns  $1500  a  year.      How  much  does  he 
earn  a  day,  if  he  works  313  days  ? 

6.  What  cost  4400  Ib.  of  coal  at  $4.60  a  ton  ? 

7.  A  house  cost  $7800,  a  barn  ft  as  much.     What  did 
both  cost  ? 

8.  A  plot  of   grass  is  3  rd.  square.     How  many  feet 
around  it  ? 

9.  747  +  138J  +  47J  +  «  +  130^  +  40  =  ? 

10.  Pineapples   are  worth  $.25  apiece.     What  will   8^ 
dozen  cost  ? 

11.  How  long  is  the  fence  that  extends  around  a  lot  14  ^ 
rods  long  and  165  ft.  wide  ? 

12.  What  number  must  be  multiplied  by  2463  to  make 
5666369  ? 

13.  11967  X  290  are  factors  of  what  multiple  ? 

14.  Quotient  4308,  divisor  28701.     Find  the  dividend. 

15.  If  I  spend  $|  for  candy  and  $T3?J  for  fruit,  what  part 
of  a  dollar  do  I  spend  ? 

16.  If   I  take  5280  from   the  sum  of   3782  and  7848, 
divide  the  remainder  by  50,  and  multiply  the  quotient  by 
19,  what  is  the  product  ? 


MISCELLANEOUS.  93 

1.  I  pay  $6  for  the  use  of  $100  for  one  year.     How 
much  do  I  pay  for  the  use  of  $300  ? 

2.  One  acre  of  corn  yields  80  bu.,  another  2|  times  as 
much,  a  third  195T5T  bu.     How  many  bushels  do  the  three 
acres  yield  ? 

3.  At  the  rate  of  9  yd.  for  $4.50,  how  many  yards  can 
be  bought  for  $120  ?     (Indicate.) 

4.  2480  -  987£J  =  ?     148J  -  96|  =  ? 

5.  297i  -  39f  =  ?     285£  +  95f  =  ? 

6.  How  much  change  will  you  receive  from  a  10-dollar 
bill,  if  you  buy  2  Ib.  of   tea  at  $.50,  18  Ib.  of  sugar  at 
5J  ct.,  and  5£  Ib.  of  beef  at  18  cents  ? 

7.  18  -  13J  +  195J  +  13J  =  ?     907  -  138}i  =  ? 

8.  2468^  -  348^  =  ?     248^  -  83£  =  ? 

9.  1694  x  395  -  2956  =  ?     2958346  -=-  297  =  ? 

10.  3J  yd.  of  ribbon  are  required  for  one  hat,  and  12|  yd. 
for  a  dress.     How  much  will  it  cost  at  $J  a  yard  ? 

11.  John  read  §  of  an  hour,  and  was  idle  £  of  an  hour. 
How  many  minutes  was  he  idle  ? 

12.  What  will  3  melons  cost,  if  £  of  a  melon  costs  15 
cents  ? 

13.  Add  105§,  294£,  135$,  and  2997|. 

14.  Subtract  899J  from  2349f . 

15.  What  is  gained  on  250  Ib.  of  sugar,  bought    at    4 
cents,  and  sold  at  5J  cents  ? 

16.  If  you  study  5^  hours  a  day  in  school,  and  Ij  hours 
at  home,  how  many  hours  will  you  study  in  40  weeks  ? 

17.  What  part  of  a  dollar  is  60  cents  ? 

18.  In  8 J  yards,  how  many  inches  ? 

19.  How  many  feet  around  a  lot  4  rd.  square  ? 
In  division,  when  is  the  quotient  1  ? 


94  ARITHMETIC. 

Sight  Work. 

1.  Reduce  to  whole  or  mixed  numbers : 

II,  ¥,  W,  alft,  II,  W,  W,  W,  -4*. 

2.  J  gallon  equals  how  many  quarts  ? 

3.  How  many  inches  in  £  ft.  +  §  ft.  +  J  ft.  ? 

4.  What  will  2  bu.  of  onions  cost,  if  a  peck  costs  $.25  ? 

5.  Paid  10  ct.  for  a  paper  of  pins,  8  ct.  for  some  braid, 
and  $.35   for  a  handkerchief.     How  much   change   do   I 
receive  from  one  dollar  ? 

Give  answers:  . 

6.  §  of  45.  9.  ft  of  121.  12.  }J  of  600. 

7.  J  of  60.  10.  ^  of  108.  13.  }f  of  136. 

8.  |  of  96.  11.  Jg  of  300.  14.  |J  of  200- 

15.  9  X  12§.  18.    15     X  10$.  21.      29J  X  11. 

16.  11  X    9J.  19.    19£  X    6.  22.      35£  X    8. 

17.  13  X     8|.  20.    30§  X  18.  23.    127§  X     6. 

24.  How  many  pints  in  33  gallons  ? 

25.  2930  -  128  =  ?  6451  -  2314  =  ?  9900  -  3647  =  ? 

26.  4J  +  7J  -  6|  =  ?     l}f  +  9J  =  ?     29J  -  11§  =  ? 

27.  108  is  a  multiple  of  what  two  numbers  ? 

28.  From  JJ  take  J.     Take  J  from  l£. 

29.  50  X  15  =  ?  34.    600  ^  ?      =  40 

30.  28  X  ?    =  196  35.      11  X  330  =  ? 

31.  18  X  ?    =  198  36.        9  X  219  =  ? 

32.  ?  X  18  =  216  37.        8  X  304  =  ? 

33.  ?  X  27  =  297 

38.  Julia  will  be  13  years  old  on  Aug.  2d  next.    In  what 
year  was  she  born  ? 

39.  What  is  the  cost  of  72  eggs  at  22  ct.  per  dozen  ? 


MISCELLANEOUS.  95 

Add: 

1.  6f,  5J,  2f  4.  3£,  4J,  8|,  4|. 

2.  4f,  2i,  8^.  5.  8f,  2*,  8,  121&. 

3.  f ,  |,  J,  J.  6.  4J,  20,  64,  71*. 

Subtract : 

7.  64JJ  -  57§.  10.  100J  -  70|J. 

8.  18JJ-7|.  11.  67A-58f- 

9.  90j|  —  39f  12.  120J  —  39T7T. 

13.  9801  is  a  multiple  of  what  two  numbers  ? 

14.  What  is  the  smallest  number  that  can  be  divided  by 
4,  6,  8,  and  12  ? 

15.  From  a  piece  of  cloth  containing  22£  yd.,  5|  yd.  were 
sold  at  one  time,  and  7 j  yd.  at  another.     How  many  yards 
were  left  ? 

16.  How  much  heavier  is  a  cheese  weighing  80|  Ib.  than 
one  which  weighs  29|J  Ib  ? 

17.  136  18.    324  19.    603  20.    958 
X  39f                 X  27£              X  124  X  784 

21.    Find  answers : 

-2479682          22.     -9637821          23.     -1503765 
20083410  70526934  7420524 

24.  How  many  hours  in  two  weeks  ? 

25.  $2155.73  +   $429.93   +   $6873.68   +   $793.94  + 
$6347.20  =  ? 

26.  How  many  rods  in  1004  yards  ? 

27.  In  1584  ft.  how  many  rods  ? 

28.  Eeduce  2646  gal.  to  barrels. 

29.  Eeduce  539  gal.  to  gills. 

30.  How  much  does  97182  exceed  17324? 

31.  250  -f-  12  =  ?     32.    945  -f-  31.     33.    770  -5-  5  =  ? 


96 


ARITHMETIC. 


Bead  and  add  : 

1. 

$1.70 

2.  $205.003 

3.  $2357.12 

4.18 

75.08 

4378.355 

.005 

123.80 

1238.638 

5.673 

785.155 

1049.287 

4. 

$14516.25 

6.  $3120.05 

6.  $7049.01 

3847.00 

18.92 

419.87 

356.73 

97148.42 

1007.89 

3578.06 

14.92 

9890.04 

75873.97 

2793.78 

874.84 

8003.89 

401.79 

6914.79 

4478.68 

91.90 

479.14 

2.85 

77891.64 

8.54 

93.99 

783.43 

319.99 

536.72 

58.19 

64.32 

.85 

901.90 

2.69 

23.03 

372.24 

.75 

7. 

$90774.81 

8.   $438.08 

9.  $75256.35 

874.94 

54.56 

207.08 

7098.41 

9389.85 

94.35 

484.01 

946.87 

745.38 

30.19 

7.83 

6975.43 

78999.02 

91.65 

98374.58 

4938.57 

348.64 

8783.94 

26.78 

9383.53 

843.54 

7.43 

13.62 

45.84 

3825.96 

98.64 

935.78 

346.29 

2834.25 

33.49 

2863.46 

536.16 

215.17 

3984.05 

75.12 

15.18 

32.53 

826.19 

226.23 

18.96 

25.22 

86.98 

REVIEW. 


I   J 

.    ..-   ^   97 


Add: 

1. 

8764 

2.  18491 

3.  98534 

4.    983 

2940 

5864 

36720 

7354 

381 

6798 

8406 

34797 

64169 

48 

42398 

9048 

495832 

57629 

4675 

68576 

1036749 

29513  ' 

75281 

473865 

5.  2019  +  8521  +  204  x  29  =  ?     (Multiply  first.) 

6.  Express  in  other  forms  ^75,  295|J,  *f  £  a,  g|. 

7.  If  8  persons  use  a  barrel  of  flour  in  27  days,  how 
long  will  it  last  4  people  ?     (Indicate.) 

8.  How  many  dollars  must  I  spend  daily  to  use  an  in- 
come of  $800  a  year  ? 

9.  1534768  -f-  216  =  ?     £  of  2520  x  91  =  ? 

10.  Sold  a  cargo  of  salt  for  $7497,  thereby  gaining  $629. 
What  did  the  salt  cost  ? 

11.  How  many  bushels  of  oats  at  $.40  must  be  given  for 
1600  bu.  of  wheat  at  $.75  a  bushel  ?     (Indicate.) 

12.  The  sum  of  two  numbers  is  247,  the  smaller  number 
being  216.     What  is  the  product  of  the  two  numbers  ? 

13.  Quotient  137,  divisor  293,  find  the  dividend. 

14.  What  number  added  to  93,248  makes  978,365  ? 

15.  What  number  has  for  its  factors  4,  9,  6,  7,  20  ? 

16.  If  I  give  $141  for  a  piece  of  cloth  containing  47  yd., 
for  how  much  must  I  sell  it  to  gain  $2  on  a  yard  ? 

17.  What  number  must  I  multiply  by  135  that  the  pro- 
duct may  be  505710  ? 

18.  How  many  days,  etc.,  in  6954  minutes  ? 

19.  184J  +  295*  +  24£  +  348  +  9634  =  ? 

20.  629J  +  3068  +  247f  +  96£  +  2963£  =  ? 

21.  What  is  an  integer  ? 


98  ARITHMETIC. 

1.  274  +  8946  +  389014  +  376  +  39845  +  3756340  =  ? 

2.  At  85  ct.  a  pound,  what  cost  89  Ib.  of  tea  ? 

3.  What  will  24  doz.  of  eggs  cost  at  3  ct.  each  ? 

4.  Dividend  972800,  quotient  208  ;  find  the  divisor. 

5.  8,  9,  12,  and  7  are  factors  of  what  multiple  ? 

6.  Working  8  hours  a  day,  how  much  will  a  man  earn 
during  this  month  at  15  ct.  an  hour  ? 

7.  3465  -f-  (36  +  12)  =  ?     9871  X  119  X  0  =  ? 

8.  529  X  0  +  1554239  -f-  216  =  ? 

9.  Bought  325  loads  of  barley,  each  load  containing  50 
bu.,  at  98  ct.  a  bushel.     What  did  the  barley  cost  ? 

10.  How  many  fourths  of  a  pound  in  396  pounds  ? 

11.  If  25  acres  of  land  cost  $2450,  what  will  £  acre  cost  ? 

12.  What  is  the  value  of  12  bales  of  cotton,  containing 
425 £  Ib.  each,  at  56  ct.  a  pound  ? 

13.  One  paper-cutter  costs  37£  ct. ;  what  will  12  dozen 
cost? 

14.  How  many  steps  of  2£  ft.  each  will  a  man  take  in 
going  3^  miles  ? 

15.  A  man  sells  2|  gross,  5j  gross,  14JJ  gross,  and  10^ 
gross  of  lead  pencils  at  36  ct.  a  dozen.     How  much  does  he 
receive  for  all  ? 

16.  28£  yd.,  6^  yd.,  40|  yd.,  and  39£  yd.  of  silk  were 
sold.     How  many  yards  were  sold  ? 

17.  To  the  sum  of  19}  and  34f  add  their  difference. 

18.  If  2  qt.  of  oil  cost  10  ct.,  what  will  2  gal.  2  qt.  cost  ? 
Divide : 

19.  3869  -v-  18  22.    289352  -f-  9G 

20.  2836  -r-  27  23.    368421  ~  125 

21.  3953  -+  82  24.     28932  -^  77 


REVIEW. 


99 


Subtract  : 

1.   17} 

2.   25^ 

3.   37f 
-18f 

4.   54| 
-15} 

5.  113T7F 
9.   63| 

6.   130$ 

7.   59§ 
-49} 

11.   580 
-98^ 

8.   575 
-  1931 

10.   76} 

-Mi 

12.   73f 

13.  100} 
-33^ 

14.   473 
-357§ 

15.  1000 
-_899| 

16.  1370 

-349^ 

17.  576^ 
-176| 

18.  888£ 
-239} 

19.  1532 

20.   131^ 

21.  295$ 
-186| 

22.  1038} 
-192j 

23.   123J 
-108} 

24.   234J 
-127} 

25.  221} 
-109$ 

29.  200f\> 
-176| 

26.  238J 
-129J 

30.  325} 
-105J 

27.   233J 
-107} 

31.   493tV 

28.  277^ 
-159J 

32.   601A 

-198|_ 

33.  322  1 
-1751 

34.   347J 

-98f 

35.   193^ 

36.   246J 
-198f 

37.  900} 

38.  1006J- 
-290} 

39.  2901f 
-190J 

40.  2063 
-249} 

7.  36 

12.  27 

17.  54 

8.  18 

13.  40 

18.  64 

9.  44 

14.  50 

19.  72 

10.  45 

15.  56 

20.  84 

11.  48 

16.  63 

21.  96 

100  ARITHMETIC. 

Multiply  by  25 : 

1.  16  ;  12  ;  24  ;  36  ;  28  ;  72  ;  48  ;  96. 
Mental  Work. 

Give  three  factors  of  : 

2.  12 

3.  16 

4.  20 

5.  24 

6.  32 

Written. 

Give  least  common  multiple  of : 

22.  2,  3,  and  4.  25.    5,  3,  and  6. 

23.  3,  2,  and  5.  26.    4,  8,  and  12. 

24.  2,  4,  and  6.  27.    5,  10,  and  16. 
Reduce  to  whole  or  mixed  numbers : 

28.  V-  31.    V-  34-    ft  37. 

29.  ^a  32.    y  35.    ^  38. 

30.  V  33.    V  36.    iffA  39. 

Mental. 

Reduce  to  improper  fractions  : 

40.  7£        44.  7^  48.  12^      52. 

41.  4f       45.  8T9T  49.  13$      53.  18f 

42.  5$       46.  9|  50.  17f      54.  124J 

43.  6|       47.  12TV  51.  9|f      55.  303J 
Divide  without  copying : 

56.  120  -:-  30  60.  720  -f-  90  64.  840  -r-  120 

57.  360  -j-  40  61.  960  -h  80  65.  960  ^  240 

58.  480-=- 60  62.  320 --40  66.  720-^360 

59.  640  -T-  80  63.  1440  -f-  120  67.  5200  ^-  130 


REVIEW.  101 

Written  Work. 

1.  A  man  buys  5  chairs  at  $9.75  each;  he  sells  them 
at  a  profit  of   50  ct.  each.     What  does    he    get  for   the 
chairs  ? 

2.  I  buy  some  lace  at  $3.05£  a  yard.     What  will  18  yd. 
cost? 

3.  $12987.032  -  $3498.107  =  ?     39870  x  273  =  ? 

4.  A  barrel  of  flour  weighs  196  Ib.     What  will  2£  bbl. 
cost  at  3  ct.  a  pound  ? 

5.  $892.06  equal  how  many  mills  ? 

6.  1387500  cents  equal  how  many  dimes  ? 

7.  At  4£  ct.  a  spool,  what  cost  3126  spools  of  thread? 

8.  Reduce  3  T.  15  cwt.  34  Ib.  6  oz.  to  ounces. 

9.  At  $1.60  for  4  Ib.  of  cinnamon,  what  will  1  oz.  cost  ? 
Add: 

10.  18J,  17f  30f  13.    248^,  26f,  950. 

11.  28TV,  14§,  290.         14.    190^,  370£,  29J. 

12.  304J,  9T7T,  95£.         15.    87|,  31J,  40J. 

16.  2963  x    27  =  ?  19.     3078506  -r-  191  =  ? 

17.  3070  X  109  =  ?  20.      2693705  +  205  =  ? 

18.  729580  x  308  =  ?  21.    97548900  -r-  113  =  ? 

22.  A  field  is  8  rd.  long  and  40  feet  wide.     How  many 
feet  around  it  ? 

23.  How  many  steps  30  in.  long  will  a   man   take    in 
walking  1£  miles  ? 

24.  In  132  ft.  how  many  rods  ?     Inches  ? 

25.  S.    T.    Smith   bought    furniture    for   $98J,    $240f, 
J,  $2096§,  and  $306TV     What  was  his  bill? 

26.  8  x  25  28.    180  X  25 

27.  25  X     6  29.    200  X  25 


102  ARITHMETIC. 


1.  13f  4-  19  J  -  13£  =  ?      4.  204  -  38}  +    16£  =  ? 

2.  121  £  +  20$  -  30    =  ?      5.  95J  -  40|  +391    =  ? 

3.  96$  +  13$  +  50J  =  ?      6.  75£  -  31    +  647$  =  ? 
Reduce  to  lowest  terms  or  to  higher  terms  : 

7.  Jft            10.    |f            13.    flfr  16.    ^  19.      ft 

8.  H            11-    Si           14«      H  17-    Jft  20«    H* 

9.  H            12.    if            15.    f&  18.      «  21-    ft* 

22.  In  3J  hhd.  how  many  quarts  ? 
I 

23.  How  many  gills  in  15  gal.  1  qt.  2  pints  ? 

24.  Reduce  1010  pints  to  gallons,  etc. 

25.  How  much  will  a  grocer  make  on  16  bu.  of  potatoes, 
if  he  buys  them  at  75  ct.  a  bushel,  and  sells  them  at  22  ct. 
a  peck  ? 

26.  In  3  da.  59  min.  how  many  minutes  ? 

27.  How  many  half  -pint  glasses  of  jelly  can  I  fill  from 
21  gallons  ? 

28.  How  many  feet  long  is  a  fence  extending   around 
a  field  12  rd.  long  and  8  rd.  wide  ? 

29.  Draw  a  square  ;  call  each  side  13£  ft.     How  many 
inches  half-way  around  it  ?     How  many  yards  around  the 
other  half  ? 

30.  At  6£  ct.  a  pound,  what  cost  150  Ib.  of  sugar  ? 

31.  In  328563  gills,  how  many  hogsheads,  etc.  ? 

32.  A  dog  runs  ^  mi.     If  he  leaps  2j  feet  each  time, 
how  many  leaps  does  he  make  ? 

33.  |  of  960408  -  243  =  ?     985073  X  209  =  ? 

34.  J  of  86400  =  ?     6370012  -s-  194  =  ? 

35.  $6401.37  +  $19587.01J  +  $29563.01^  =  ? 

36.  38420  -r-  250  =  ? 

37.  1289626  -5-  352  =  ? 


MISCELLANEOUS.  103 

1.  1504  mills  equal  how  many  dollars  ? 

2.  How  many  yards  in  2£  miles  ? 

3.  At  $f  a  yard,  what  cost  16  yards  of  muslin  ? 

4.  What  will  it  cost  to  dig  a  ditch  Ij  miles  long,  at 
75  ct.  a  rod? 

5.  How  many  feet  of  moulding  will  be  required  for  a 
room  16  ft.  long  and  14  feet  wide  ?     (Illustrate.) 

6.  John  steps  1  \  ft.  at  each  step ;  how  many  steps  will 
he  take  in  walking  66  rods  ? 

7.  George's  kite-string  was  120  yd.  long ;  he  lost  180  ft. 
of  it.     How  many  inches  remained  ? 

8.  At  $.06J  a  spool,  what  cost  3126  spools  of  silk  ? 

9.  How  many  quarter-dollars  in  $19£  ? 

10.  In  210  half -dimes,  how  many  dollars  ? 

11.  From  a  board  22  ft.  long,  a  carpenter  sawed  3  ft. 
5  in.  How  much  remained  ? 

12.  How  many  inches  in  \  of  12  yards  ? 

13.  What  will  it  cost  to  fence  a  farm  J  of  a  mile  square, 
at  95  ct.  a  foot  ? 

14.  32840  X  490  =  ?     1093457  X  47  =  ? 

15.  19£  +  13}  +  27  =  ?          18.   270}  +  9|  +  2^  =  ? 

16.  31|  -  10J  +  30^T  =  ?      19.    190  -  38^  +  1J  =  ? 

17.  240J  -  91|  +  987  =  ?      20.    19J  +  2£  +  360  =  ? 

21.  A  tree  is  4  ft.  10  in.  high.     How  many  inches  must 
it  grow  to  measure  73  feet  in  height  ? 

22.  At  18  ct.  each,  what  will  Mrs.  Gale  pay  for  12759 
salt-barrels  ? 

23.  If  the  blackboard  is  5  yd.  long  and  6  ft.  3  in.  wide, 
how  many  yards  around  it  ? 

24.  How  many  feet  in  4  rods  ? 


104  ARITHMETIC. 

Compound  Numbers. 

1.  From  9  rd.  1  ft.  take  2  rd.  2  ft. 

2.  Find  the  difference  between  5  yd.  2  ft.  4  in.  and  16  rd. 

3.  Take  12  yd.  2  ft.  from  15  yd.  1  ft. 

4.  What  taken  from  25  gal.  1  qt.  leaves  6  gal.  3  qt.  ? 

5.  50  min.  30  sec.  —  16  min.  45  sec.  =  ? 

6.  Find  the  sum  of  187  T.,  116  T.  1314  lb.,  147  lb., 
53  T.  711  lb.,  21  T.  35  lb. 

7.  Add  93  lb.  15  oz.,  19  lb.  6  oz.,  28  lb.,  32  lb.  22  oz., 
6  lb.  9  oz.,  21  oz. 

8.  2  gal.  2  qt.  1  pt.  +  16  gal.  3  qt.  1  pt.  +  80  gal.  1  qt. 
+  25  qt.  1  pt.  =  ? 

9.  How  many  hours,  minutes,  and  seconds  in  4  hr.  12 
min.  22  sec.,  15  hr.  26  min.  29  sec.,  45  min.  15  sec.,  35  se^.  ? 

Subtract  : 

1.  35  da.  2  hr.  1  min.  3.    17  gal.  2  pt. 

5  da.  5  hr.  5  min.  8  gal.  3  qt.  1  pt. 

2.  120  bu.  4.    100  mi.  15  rd. 

45  bu.  2  pk.  5  qt.  84  mi.  24  rd. 

Find  results  : 
1.    18  lb.  14  oz.  12  dr.  3.    18  gal.  3  qt.  1  pt. 

__  9  _          9 


37  lb.    3  oz.  14  gal.  1  qt.  1  pt. 

2.    15  yd.  3  ft.  6  in.  4.    25  bu.  2  qt.  1  pt. 

—  7  yd.  2  ft.  7  in.  +  14  bu.  2  qt. 

5.  193  gal.  2  qt.  1  pt.  +  ?  =  230  gal.  3  qt. 

6.  2  hhd.  2  gal.  2  gi.  -  ?  =  1  hhd.  1  gi. 


REVIEW.  105 

1.  What  cost  16  chests  of  tea,  each  weighing  52  Ib.  at 
ct.  a  pound  ? 

2.  A  single  rail  is  two  rd.  long;  how  many  rails  will 
be  required  to  lay  a  mile  of  railroad  ? 

3.  From  $10,009  take  $9.073.     648730  X  207  =  ? 

4.  Sold   a   horse  for   $145.27,   which  is  $37.69   more 
than  it  cost ;  what  did  it  cost  me  ? 

5.  How  many  barrels,  etc.,  in  24680  gills  ? 

6.  John  King  bought  a  pair  of  horses  for  $480,  a  har- 
ness for  $80.50,  and  a  carriage  for  $150  less  than  he  paid 
for  both  horses  and  harness.     What  was  the  cost  of  the 
carriage  ? 

7.  6J  +  9|  +  18J  +  120£  +  960f  =  ? 

8.  A  of  990  X  f  of  560  =  ?     2963  -  981^  =  ?     . 

9.  What  cost  a  pound  of  beef,  if  894  Ib.  cost  $80.46  ? 

10.  A  farmer  sells  120  bu.  of  wheat  at  $1.12£  a  bushel, 
for  which  he  receives  27  bbl.  of  flour.     What  does  the  flour 
cost  him  a  barrel  ?     (Indicate.) 

11.  36  Ib.  of  tea  cost  $23.40.     What  cost  5  pounds  ? 

12.  63  X  ?  =  93840.     99  X  33847  =  ? 

13.  Add  120  dollars,  85  dimes,  9  cents,  7  mills,  44  hak- 
dimes,  and  one  eagle. 

14.  A  man  bought  horses  for  $556  a  pair ;  how  many 
horses  can  he  buy  for  $20016  ? 

15.  At  $7  a  ton,  what  cost  500  Ib.  of  hay  ? 

16.  A  house  cost  $11622,  which  is  13  times  as  much  as 
the  lot  cost.     What  did  the  lot  cost  ? 

17.  Find  4  factors  of  1270,  1960,  340,  230. 

18.  In  2  mi.  5  rd.,  how  many  inches  ? 

19.  Find  the  sum,  difference,  and  product  of  294  and  79. 


106  ARITHMETIC. 

GENERAL    REVIEW  PROBLEMS. 

Sight  Work. 

1.  3|  +  44  +  8  =  ?     24  +  6J  -  1J  =  ? 

2.  Take  3J  +  9£  +  3  from  44. 

3.  How  many  pounds  of  hay  in  7£  tons  ? 

4.  How  much  fringe  will  be  needed  to  go  around  a  rug 
9J  ft.  by  3£  ft.  ? 

5.  What  will  the  fringe  cost  at  20  ct.  a  yard  ? 

6.  Nutmeg  is  worth  $.04^  an  ounce.     What  will  j  of  a 
pound  cost  ? 

7.  From  f  of  63  take  £  of  42. 

8.  Divide  3  by  14.     11  by  21.     16  by  30. 

9.  A  boy  picked  2  bu.  of  cherries  ;  he  sold  J  of  them  at 
5  ot.  a  quart.     What  did  he  receive  for  them  ? 

10.  William  owes  $42f  for  his  pony.     He  saves  $2^  a 
week.     If  he  pays  what  he  saves  in  a  month,  what  does  he 
still  owe  for  the  pony  ? 

11.  Change  to  simplest  form  J£,  ^T,  $$,  f  f,  ^fr. 

12.  -i-2±  =  ? 


13.  33  -s-  5J  =  ?     22  -*-  3J  =  ?    21  -^  4J  =  ? 

14.  What  is  a  fraction  ?     Factor  ?     Product  ? 

15.  168  is  a  multiple  of  what  two  numbers  ? 

16.  From  12J  take  9f  .     120  -  13J  =  ? 

17.  12  X  13  -  9  =  ?     120  -v-  5  X  7  =  ? 

18.  4j  +  gj.  _  6  =  ?     27  +  18J-  +  40J  =  ? 

19.  Give  four  factors  of  96,  48,  56,  32. 

20.  8  X  9J  =  ?     10  X  30f  =  ?     |  of  1080  =  ? 

21.  6|  X  24  =  ?     8i  X  35  =  ?     11  X  ?  =  154. 

22.  How  many  feet  in  6  rods  ? 


MISCELLANEOUS.  107 

1.  How  many  cents  in  4  double  eagles  ? 

2.  How  many  half-dimes  ought  I  to  receive  in  exchange 
for  1£  eagles  ? 

3.  Eeduce  to  cents  and  add  :  4  eagles,  30  dollars,  5  half- 
dollars,  3  quarter-dollars,  12  dimes,  and  60  half-dimes. 

4.  How  many  cents  in  $642j  ? 

5.  J  of  270  +  J-  of  1960  —  f  of  560  =  ? 

6.  18J-  +  13J  +  19  =  ?         10.    131  -  10£  +  49  =  ? 

7.  204f-160^+140^=?     11.    20£  +  39J  +  12  =  ? 

8.  9034  -  1041^  +  |  =  ?     12.    130  -  29£  -  13J  =  ? 


14.  In  1568  oz.  how  many  pounds  ? 

15.  How  many  half-ounce  weights  can  be  made  from 
98  Ib.  of  brass  ? 

16.  What  cost  58£  cwt.  of  pork  at  11  cents  a  pound  ? 

17.  For  $98.44,  how  many  pounds  of  butter  can  be  bought 
at  27  ct.  a  pound  ? 

18.  In  a  carload  of  potatoes  were  330  bushels.    I  bought 
J  of  them  at  37  ct.  a  bushel.     What  did  they  cost  me  ? 

19.  At  38  ct.  a  pound,  what  cost  97£  Ib.  of  coffee  ? 

20.  701  X  391  -  44506  =  ? 

21.  A  boy  having  600  marbles,  gave  away  £  of  them, 
lost  J  of  them,  and  sold  the  remainder  at  the  rate  of  2  for 
a  cent.     How  much  money  did  he  receive  ? 

22.  1135  +  209J  +  28  +  129$  -  201  =  ? 

Find  quotients  : 

23.  28326-^-58. 

24.  39823  -f-  73. 

25.  98463-^215. 

26.  38848  -j-  79. 

27.  33333-^99. 


108 

ARITHMETIC. 

Subtract  : 

1. 

256375 

2.     189730 

3.    245793 

—  78597 

-  98751 

-  104832 

4. 

23121 

5.      9675 

6.    243967 

—  ? 

_  9 

_  9 

8573 

7356 

145578 

7. 

-  57869743 

8.  -20503742 

9.     250606 

490132001 

910602053 

-  172739 

10. 

149682356 

11.   1200000*0 

12.   -  143654 

-  37035874 

990909 

1950000 

13. 

70000000 

14.  -15357580 

15.  340302056 

69570649 

987543123 

259686765 

16. 

843 

17.      3927 

18.    732685 

2692 

83528 

6128 

74863 

9 

624689 

738342 

23687 

9 

9 

94649 

749309 

486903 

38652 

9708 

2161037 


380241 


2905790 


19.  2435693  -  856487  =  ? 

20.  8754321  -  ?  =  1235697 

21.  ?  -  258721  =  6492130 

22.  48325  -  ?  =  45993 

23.  ?  -  87543  =  123473 

24.  594789-7  =  239896 

25.    Subtrahend    84798,    remainder    109878,    find     the 
minuend. 


MISCELLANEOUS.  109 

Written  Work. 

1.  Change  3960  in.  to  rods,  etc. 

2.  |  of  a  barrel  of  vinegar  leaked  out.    How  many  pint 
bottles  can  be  filled  from  what  remained  ? 

3.  Write  in  Arabic  notation  one  million,  one  hundred 
six  thousand,  five  hundred  nineteen. 

4.  From  37  bu.  how  many  pints  of  walnuts  can  be  sold  ? 
Find  the  cost  at  8  ct.  a  pint. 

5.  I  step  24  in.  in  one  step.    How  many  steps  do  I  take 
in  going  around  the  school  lot,  if  it  is  198  by  132  feet  ? 

6.  Paid  $7360  for  46  horses  ;  what  was  the  cost  of  one 
horse  ? 

7.  Find  the  product  of  3496  and  4857. 

8.  16/T  +  13}  +  391  =  ?     241J  +  39£  -  10H  =  ? 

9.  Paid  $7260  for  a  house  and  lot ;  the  house  cost  $  of 
it.     What  did  the  lot  cost  ? 

10.  19£  +  lOjj-  +  16£  -  29ft  =  ? 

11.  |  +  J  +  J  +  ft  +  247  =  ?     29703  X  43  =  ? 

12.  Write  a  mixed  number,  and  change  it  to  another 
form. 

13.  Find   the   cost  of   3£  tons  of  hay  at  £  ct.  for  one 
pound. 

14.  |  equals  how  many  270ths  ? 

15.  What  part  of  500  is  200  ? 

16.  Subtrahend  341^,  remainder  250$ .     Find  the  miss- 
ing term. 

17.  Reduce  45649  oz.  to  higher  denominations. 

Divide : 

18.  3869846  by  2832. 

19.  2863521  by  983. 

20.  3612152  by  76. 


110  ARITHMETIC. 

Multiply : 

1.  378  X  35  10.  4029  X  867  X    59 

2.  367  X  24  11.  4705  X  395  X    87 

3.  434  X  52  12.  521  X  742  x  835 

4.  805  X  45  13.  471  X  235  X  749 

5.  1234  x      14  14.      905  X  403  X  607 

6.  2135  X    127  15.      632  x  320  X  478 

7.  3598  X    103  16.      876  X  324  X  903 

8.  28453  X    897  17.    1286  X  521  x  632 

9.  1925  X  5076  18.    2010  X  837  X  156 

19.  Multiplicand  1875,  multiplier  906 ;  what  is  the  pro- 
duct? 

20.  Product  468750,  multiplier  625 ;  what  is  the  multi- 
plicand ? 

21.  Multiple  66516,  one  factor  172;    what  is  the  other 
factor  ? 

Divide : 

22.  4352  -f-  32  29.  210522  -r-  1248 

23.  5438 -f-  51  30.  847916 -r- 2016 

24.  8877  -T-.  77  31.  869827  -?-  5068 

25.  20492  -f-  168       32.   851724  -5-  5028 

26.  42642  -r-  194       33.   1778136  -v-  1923 

27.  84774  -j-  246       34.   3855810  -r-  2135 

28.  147380  -f-  690       35.  11080268  -r-  756 

36.  Multiple  611604,  one  factor  756;  find  the  other 

factor. 

4 

37.  Divisor  354,  dividend  95580 ;  find  the  quotient. 

38.  Divisor  812,  quotient  1243  ;  what  is  the  dividend  ? 

39.  Dividend  87654,  divisor  203 ;  find  the  quotient. 

40.  Dividend  75432,  quotient  123 ;  what  is  the  divisor  ? 


REVIEW.  Ill 

Solve  at  sight  as  many  as  possible : 

1.  Reduce  94  to  a  fraction  whose  denominator  is  7. 

2.  Change  247  to  the  form  of  a  fraction. 

3.  Express  in  its  simplest   form   the  quotient   of   56 
divided  by  63. 

4.  From  |  take  f .     From  1J  take  TV 

5.  11  -  }  =  ?     «  -  A  =  ?     9J  -  2|  =  ? 

6.  Subtrahend  8^,  remainder  15  J ;  what  is  the  minuend? 

7.  (20  -  16J)  +  (24|  -  13|)  =  ?     9^  -  7|  =  ? 

8.  A  man  earns  $7-J  a  week;    his  expenses  are  $4f. 
How  much  does  he  save  ? 

9.  What  must  be  added  to  the  sum  of  $  and  7|  to 
make  20  ? 

10.  £  of  my  money  is  in  bills,  £  in  silver,  and  the  rest 
in  gold.     What  part  is  in  gold  ? 

11.  Mary  has  f  10£  in  50-cent  pieces  ;  how  many  has  she  ? 

12.  £  pound  of  tea  cost  37£  ct. ;  how  much  will  2  pounds 
cost? 

13.  At  16  ct.  a  pound,  how  much  will  3|  lb.  of  meat  cost  ? 

14.  A  of  50  +  T7*  of  60  ==  ?     29587  X  107  =  ? 

15.  6J  +  8|  +  9  =  ?  22.        |  -  ?      =  lOf 

16.  80  -  37f  +  10  =  ?         23.    84     -  3l£  =  ? 

17.  29^  -  11§  +  6  =  ?         24.      6J  -  ?       +    3    =  7£. 

18.  ?  -  7J  =  9|.  25.      9J  +    2£  +    1J  =  ? 

19.  ?      +  13£  =  20.  26.      2|  -        §  +  is    =  ? 

20.  17£  —  ?      =  4.  27.    24    +  30£  -  20J  =  ? 

21.  25    -  ?      =  17^.          28.    16    _  13£  +  26    =  ? 

29.  Product  187,  multiplier  11 ;  find  the  multiplicand. 

30.  Product  136,  multiplicand  7  ;  find  multiplier. 

31.  ?  x  12  =  1728. 


112  ARITHMETIC. 

1.  What  will  15  bu.  2  pk.  2  J  qt.  of  nuts  bring,  at  12  ct. 
a  quart  ? 

2.  What  number  is  that  to  which,  if  you  add  18|,  the 
sum  will  be  97?  ? 

3.  A  boy  sold  his  book  for  $  3J,  which  was  $£  less  than 
he  paid.     What  did  it  cost  him? 

4.  What  part  of  49  is  27  ?     Of  88  is  44  ? 


6.  How  many  packages  of  8  oz.  each  can  be  made  from 
100  cwt.  of  cinnamon  ? 

7.  At  18  ct.  a  pound  for  roast-beef,  what  will  5  Ib.  7  oz. 
cost? 

8.  What  cost  349  Ib.  of  sugar  at  5£  ct.  for  one  pound  ? 

9.  19|  +  15|  +  17f  =  ?     2960  x  91  =  ? 

10.  At  12  ct.  a  pound,  what  cost  18|  Ib.  of  cheese  ? 

11.  When  J  of  a  year  has  passed,  how  many  days  re- 
main ?     How  many  hours  ? 

12.  At  5  ct.  a  pint,  what  will  a  barrel  of  vinegar  cost  ? 

13.  What  will  625  oysters  cost  at   one  dollar  for   100 
oysters  ? 

14.  Change  1260  pt.  to  barrels,  and  find  the  cost  at  $22£ 
a  barrel  ? 

15.  4£  hours  of  a  day  have  passed  ;  how  many  minutes 
remain  ? 

16.  2990  is  a  multiple  of  what  3  numbers  ? 

17.  I  buy  1  bu.  of  pears  for  $2  and  sell  them  so  as  to 
gain  $2.20.     How  much  does  one  peck  bring  ? 

18.  6  X  998  -f-  39  =  ?     450^  -  340f  =  ? 

19.  25796  -*-  137  =  ? 

20.  3576  X  1247  =  ? 


REVIEW.  113 


2.  518JJ  -  309f  J.  5.    802TV  -  128if  . 

3.  532T\  -  227£§.  6.   132f    +  719  j. 

7.  How  many  pounds  of  butter  at  33  ct.  a  pound  can 
be  bought  for  55  Ib.  of  tea  at  78  ct.  a  pound  ?     (Indicate.) 

8.  A  pedler  bought  491  yd.  of  cloth  at  $.81  a  yard. 
He  used  29  yd.,  and  sold  the  rest  for  $.95.     How  much 
did  he  gain  ? 

9.  A  man  exchanged  159  cords  of  wood,  at  $5  a  cord, 
for  a  horse  valued  at  $144,  and  the  balance  in  sheep  at  $3 
each.     How  many  sheep  did  he  get  ? 

10.  What  cost  9  hats,  if  5  cost  $12.25  ? 

11.  To  what  number  must  three  times  27  be  added  to 
make  120  ? 

12.  Find  the  cost  of  11  Ib.  4  oz.  of  tea  at  48  cents  for 
one  pound  ? 

13.  A  flag-pole  180  ft.  high  broke  off  £  way  up.     How 
many  yards  broke  off  ? 

14.  200  +  143}f  -  39}f  =  ? 

15.  (24}  -  12|)  +  (if  +  f)  -  ? 

16.  1958£  -  496H  +  97  =  ? 

17.  If  a  man's  pulse  beats  72  times  in  a  minute,  how 
many  times  will  it  beat  in  2£  hours  ? 

18.  A  miller  buys  12890  pounds  of  wheat  at  the  rate  of 
90  cents  for  60  pounds.     How  much  does  he  pay  for  it  ? 

19.  If  36  men  can  do  a  piece  of  work  in  84  days,  how 
long  will  it  take  42  men  to  do  it  ?     (Indicate.) 

20.  81}  +  13i  -  27i  =  ? 

21.  100  -  69^  +  38|  =  ? 

22.  120i  -  75^  +  65|  =  ? 

23.  300  -  18J  -  59J  =  ? 


114  ARITHMETIC. 

1.  Define  fraction ;  improper  fraction,  and  give  examples. 

2.  MjVi11  equals  what  mixed  number  ? 

3.  Eeduce  }Jf  to  its  lowest  terms. 

4.  Change  £,  f ,  f ,  £  to  fractions  having  a  least  common 
denominator. 

5.  Change  16  to  fourths.     5£  to  twelfths. 

6.  From  seven  million,  sixty-three  thousand,  eight  hun- 
dred six,  take  six  million,  forty-five  thousand  and  thirty- 
seven,  and  multiply  the  result  by  three  hundred  seventeen. 

7.  Mrs.  A.  L.  Jones  bought  a  sewing-machine  for  $65. 
She  paid  $20  cash.     How  many  months  will  it  take  her  to 
pay  the  rest,  if  she  pays  $5  a  month  ? 

8.  Mr.  Bradley  Phillips  sold  5  lots  at  $864  each,  then 
purchased  a  house  and  lot  for  $2563;  how  much  did  he 
have  left  ? 

9.  What  part  of  2  bu.  is  1  bu.  4  quarts  ? 

10.  Lulu  Lane  paid  $20  for  15  piano  lessons,  and  $35 
for  20  violin  lessons.     What  did  each  lesson  cost  ? 

11.  Add  f ,  A,  6f,  17JJ.     31*  -  27f  +  17H  =  ? 

12.  The  quotient  is  151,  the  divisor  364,  the  remainder 
39.     Find  the  dividend. 

13.  When  you  change  J  to  §g  do  you  change  the  value  ? 
How  do  you  affect  the  number  of  parts  ?     How  do  you 
affect  the  size  of  the  parts  ? 

14.  Eeduce  13  bu.  2  pk.  7  qt.  1  pt.  to  pints. 

15.  How  many  feet  in  9|  miles  ? 

16.  Miss  Marie  Hunt  paid  $38.50  for  20  reading  lessons. 
How  much  did  she  pay  for  2  lessons  ? 

17.  103  X  2894  =  ? 

18.  39£  -  13f  +  15£  =  ? 

19.  384526  -5-  169  =  ? 


REVIEW. 


115 


Mental  Work. 

Add: 

1. 

52  + 

65 

8. 

950 

+ 

790 

15. 

31  + 

22 

+  34 

2. 

44  + 

77 

9. 

190 

+ 

320 

16. 

20  + 

30 

+  81 

3. 

26  + 

82 

10. 

180 

+ 

450 

17. 

10  + 

43 

+  62 

4. 

31  + 

93 

11. 

120 

+ 

680 

18. 

14  + 

21 

+  16 

5. 

57  + 

95 

12. 

360 

+ 

590 

19. 

42  + 

24 

+  40 

6. 

68  + 

73 

13. 

780 

+ 

270 

20. 

49  + 

17 

+  20 

7. 

93  + 

38 

14. 

240 

+ 

660 

21. 

37  + 

25 

+  61 

Subtract  : 

22. 

65- 

18 

29. 

650 

— 

290 

36. 

231 

— 

165 

23. 

74- 

49 

30. 

410 

— 

320 

37. 

723 

— 

184 

24. 

82  - 

60 

31. 

330 

— 

250 

38. 

656 

— 

378 

25. 

93- 

27 

32. 

720 

— 

160 

39. 

964 

— 

197 

26. 

63- 

19 

33. 

224 

— 

35 

40. 

179 

— 

145 

27. 

55  - 

37 

34. 

421 

— 

187 

41. 

683 

— 

362 

28. 

49  - 

23 

35. 

542 

— 

439 

42. 

731 

— 

719 

Multiply  : 

43. 

89  x 

2 

50. 

210 

X 

8 

57. 

96 

X 

25 

44. 

56  X 

3 

51. 

320 

X 

9 

58. 

25 

X 

84 

45. 

94  x 

4 

52. 

360 

X 

3 

59. 

18 

X 

25 

46. 

72  x 

5 

53. 

470 

X 

2 

60. 

36 

X 

25 

47. 

62  x 

7 

54. 

1200 

X 

6 

61. 

25 

X 

48 

48. 

42  X 

8 

55. 

2500 

X 

3 

62. 

25 

X 

33 

49. 

81  X 

9 

56. 

2100 

X 

4 

63. 

320 

X 

25 

Divide  : 

64. 

175- 

5 

71. 

240 

-f- 

12 

78. 

1680 

-^_ 

210 

65. 

192- 

4 

72. 

520 

-f- 

13 

79. 

2250 

-£- 

250 

66. 

196- 

6 

73. 

600 

-i- 

15 

80. 

1890 

-i- 

270 

67. 

189- 

3 

74. 

700 

-i. 

14 

81. 

1160 

-r- 

290 

68. 

406- 

7 

75. 

640 

-f- 

16 

82. 

1900 

-f- 

380 

69. 

174- 

3 

76. 

680 

-i- 

17 

83. 

1560 

_i- 

260 

70. 

244  — 

4 

77. 

720 

-f- 

18 

84. 

2080 

-f. 

520 

116  ARITHMETIC. 

Test  Work. 

1.  Copy  and  add :  695,  378,  26,  409,  825,  6. 

2.  482  X  743  -T-  216  -  647  =  ? 

3-  (i  +  H)-(A  +  *)- 

4.  Five  boxes  of  oranges  contained  156  oranges  each, 
and  were  sold  at  $3  per  hundred.     Find  the  amount  of 
money  received. 

5.  A  piece  of  cloth  was  sold  for  $112.70  at  $2.45  per 
yard.     How  many  yards  did  the  piece  contain  ? 

6.  From  7$  yards  of  cloth  5^  were  sold.     How  much 
remained  ? 

7.  Add  J,  I,  J,  A,  3,  7,  ft,  4. 

8.  How  many  hours  in  this  month  ? 

9.  How  do  you  reduce  dollars  to  cents  ? 

10.  How  do  you  reduce  mills  to  dollars  ? 

11.  Define  multiplication,  quotient,  product. 

12.  Change  6£  miles  to  rods. 

13.  When  do  you  use   short   division   and  when   long 
division  ? 

14.  What  do  you  do  when  the  partial  dividend  will  not 
contain  the  divisor  ? 

15.  How  many  pounds  of   butter  at  15  cents  a  pound 
will  pay  for  9  boxes  of   berries  at  $.25  a   box,  and  25 
pounds  of  sugar  at  9  cents  a  pound  ? 

16.  Write  in  figures  one  million,  six  thousand  five. 


CHAPTER    III. 


BILLS  AND  ACCOUNTS. 


1.    A  receipted  bill. 
MR.  JOHN  D.  WILSON 


SYRACUSE,  Jan.  1,  1895. 
Bought  of  H.  E.  BARRETT. 


16  yd.  Silk 

@  $1.50 

$24 

00 

6  yd.  Irish  Linen 

"       .60 

3 

60 

4  pair  Hose 

"       .50 

2 

00 

1  Cane  Seat  Rocker 

4 

00 

9  yd.  Lace 

"       .50 

4 

50 

$38 

10 

Received  Payment,  H.  E. 

BARRETT. 

Mr.  John  D.  Wilson  is  the  debtor,  and  H.  E.  Barrett  the 
creditor. 

The  bill  is  a  written  statement  of  Mr.  Wilson's  account. 

It  is  a  receipted  bill  because  the  creditor,  Mr.  Barrett, 
has  acknowledged  in  writing  that  he  has  received  payment. 

Study  the  form  of   the  bill,  and  tell  what  things  are 
necessary  in  every  receipted  bill. 

If  Mr.  Wilson  had  paid  the  money  to  Mr.  Barrett's  clerk 
or  collector,  how  could  it  have  been  receipted  ? 

117 


118  ARITHMETIC. 

2.  Mr.  John  Q.  Adams  buys  of  D.  McCarthy  &  Co.  : 

4  pounds  of  coffee  at  27  cents  a  pound, 
18  pounds  of  sugar  at  5£  cents  a  pound, 

5  gallons  of  molasses  at  60  cents  a  gallon, 
16  pounds  of  rice  at  8J  cents  a  pound. 

Make  out  the  bill. 

3.  James  Smith,  farmer,  sold  Richard  Dunn,  grocer,  the 
following : 

6  barrels  of  potatoes  at  $1.80  a  bbl., 

2  tons  of  hay  at  $16  a  ton, 

3  cords  of  wood  at  $4  a  cord, 

360  pounds  of  butter  at  24£/  a  pound. 
Make  a  receipted  bill. 

4.  Syracuse,  Dec.  5,  1894.     Edward  Smith  sold  B.  M. 
Watson  65  yd.  Brussels  carpet  at  $1.25 ;  24  yd.  oil  cloth  @ 
35/ ;  one  dozen  pair  of  merino  hose  @  $3.50 ;   2  willow 
chairs  @  $4.50.     Make  bill,  find  the  footing,  and  properly 
receipt  it. 

5.  Make  out  a  bill  of  groceries.     Foot  it,  and  receipt  it, 
with  F.  H.  Mead  as  creditor  and  Wm.  H.  Scott  as  debtor. 

To  THE  TEACHER.  —  See  that  the  prevailing  prices  are 
used,  and  that  the  quantities  are  consistent. 

6.  J.  H.  Acker  bought  of  II.  A.  Strong  of  San  Francisco, 
the  following  articles:  15  bbl.  flour  @  $8.00;  6  tubs  of 
butter,  120  pounds  in  a  tub,  at  24  cents  a  pound ;  5  barrels 
of  beef,  200  Ib.  to  the  barrel,  at  5/ ;  25  sacks  of  flour  @ 
95/;   450  pounds  of   ham  at  11  J/.      Make  out  bill,  and 
receipt  it. 

7.  Make  out  a  bill  of  hardware,  another  of  groceries, 
and  another  of  dry  goods. 

8.  Make  out  a  bill  of  goods  bought  at  a  shoe  store  ;  at  a 
stationer's ;  at  a  furniture  store. 


INDICATED   WORK.  119 

Indicate  the  operations  and  find  the  results  : 

1.  The  sum  of  26  and  50,  added  to  their  difference. 

2.  The  sum  of  26  and  50,  multiplied  by  their  difference. 

3.  The  sum  of  26  and  50,  divided  by  their  difference. 

4.  The  sum  of  26  and  50,  less  their  difference. 

5.  Divide  the  product  of  9  times  112  times  16,  by  the 
product  of  28  times  18. 

6.  The  sum  of  two  numbers  is  6943.     The  greater  is 
587.     What  is  the  less  ? 

7.  At  the  rate  of   8    pencils  for  48  cents,  how  many 
cents  will  10  pencils  cost  ? 

8.  At  the  rate  of   8  pencils  for  48  cents,  how  many 
pencils  can  be  bought  for  $1.02  ? 

9.  If  a  man  is  52  years  of  age  now,  how  old  was  he  26 
years  ago  ?     How  old  will  he  be  in  26  years  ? 

10.  How  many  dozen  eggs  at  24  cents  a  dozen,  can  be 
bought  for  $7.20  ? 

11.  If  16  horses  cost  $1280,  what  will  19  horses  cost  ? 

12.  From  a  flock  of  130  sheep,  56  were  sold,  and  after- 
ward 48  were  purchased ;  how  many  sheep  in  the  flock  ? 

13.  How  many  barrels  of  flour,  at  $5.80  a  barrel,  will 
pay  for  850  pounds  of  maple  sugar  at  15/  a  pound  ? 

14.  If  I  have  $36,  and  pay  all  but  $16  for  cloth  at  $1.50 
a  yard,  how  many  yards  can  I  buy  ? 

15.  John  had  $3,  Henry  4  times  as  much,  and  Charles 
J  as  much  as  Henry.     How  much  had  all  ? 

16.  If  I  have  $18,  and  buy  2  tons  of  coal  at  $4.50  a  ton, 
and  2  cords  of  wood  at  $2.50  a  cord,  how  much  money  will 
I  have  left  ? 

17.  John  had  $76J  ;  he  deposited  $75  in  the  bank,  and 
then  earned  $28*.     How  much  money  had  he  ? 


120  ARITHMETIC. 

ADDITION  AND  SUBTRACTION  OF  FRACTIONS. 

1.  From  a  cask  of   oil  containing   42  gal.,  a  merchant 
sells  9£  gal.,  15}  gal.,  and  7£  gal.     How  much  remains  in 
the  cask  ? 

2.  If  7^  feet  are  subtracted  from  a  rod,  how  many  feet 
will  remain  ? 

3.  A  farmer  brought  to  market  3J  bushels  of  raspber- 
ries, 2}  bushels  of  blackberries,  and  3j  bushels  of  currants. 
How  many  bushels  of  berries  did  he  bring  to  market  ? 

Add: 


4.  324J 

5.  695? 

6.  1694J 

7.  2698^, 

593} 

284$ 

2436J 

2963J 

282^ 

989j 

9843f 

2956? 

MULTIPLICATION   OF  FRACTIONS. 

Oral  Work. 

1  apple  multiplied  by  4  =  4  apples. 

3  apples  multiplied  by  4  =  12  apples. 

J  multiplied  by  4  =  J. 

f  multiplied  by  4  =  |. 

|  multiplied  by  3  =  T6T. 

1.  5  times  T\  =  ?     5  times  T2T  =  i^. 

2.  6  times  1  =  |J.     4  times  f\  =  ? 

3.  6  times  ^  =  1^.     ^  multiplied  by  6  =  ? 

4.  At  $}  each,  what  will  8  books  cost  ? 

5.  If  a  horse  eat  f  of  a  bushel  of  oats  a  week,  how  many 
bushels  will  he  eat  in  10  weeks  ? 

6.  Multiply  $5i  by  2  ;  by  3  ;  by  4. 

7.  Multiply  these  fractions  by  3,  and  give  products  in 
simplest  form  :  f,  f,  f,  f,  f,  £,  f,  2£,  3J. 


MULTIPLICATION  ^F^^A^TiS^'S.  l  121 


8.  Multiply  the  fractions  in  Ex.  7  tJy^SjDy  6  ;  by  10  ; 
and  give  products  in  simplest  form. 

9.  J  of  6  =  ?     f  of  6  =  ? 

10.  §  of  a  number  is  how  many  times  J  of  it  ? 

11.  If  a  pound  of  tea  costs  48  cents,  what  will  £  of  a 
pound  cost  ?     What  will  f  of  a  pound  cost  ? 

12.  |  of  12  =  ? 

SOLUTION.  —  J  of  12  =  *£  =  3. 

f  of  12  =  3  X  3  =  9.    ^4ras. 

13.  f  of  7  =  ? 
SOLUTION.  —  J  of  7  =  J. 

|  of  7  =  5  times  J  =  ^  =  4$.    J?*s. 

NOTE.  —  |  o/  7  is  the  same  as  f  times  7,  and  the  product 
is  the  same  as  7  times  f  . 

14.  f  of  5  =  ?     ft  of  4  =  ?     |  of  3  =  ?     §  of  6  =  ? 

15.  $10  multiplied  by  |  =  ?     ^  X  10  =  ? 

16.  f  times  8  =  ?     4xf  =  ?     f  X  4  =  ? 

17.  How  much  is  %  of  J  of  an  inch  ?     (Illustrate.) 

18.  Illustrate  that  \  of  £  of  an  apple  is  J  of  an  apple. 

19.  Multiply  f  by  J  ;  f  by  ±;  £  by  4  ;  J  by  f 

20.  How  much  is  J  of  }  ?    f  of  f  ?    J  of  f  ?    J  of  ft  =  ? 

21.  A  man  owned  f  of  a  farm,  and  sold  £  of  his  share. 
What  part  of  the  farm  did  he  sell  ? 

22.  James  had  $|,  and  John  1  as  much.     How  much 
had  both? 

23.  If  a  pound  of  tea  costs  $|,  what  will  £  Ib.  cost  ? 

24.  |  X  §  =  ?     3X5  =  ?     T%  X  J  =  ? 

25.  f  X  J  =  ?     jXi  =  ?        JX|  =  ? 

26.  Find  §  of  |  ^  of  J  ;  of  ft  ;  of  ft. 

27.  Find  f  of  6  ;  of  9  ;  of  12  ;  of  15. 


122  ARITHMETIC. 

28.    }  of  |  =  ?    (Problem.)         29.    T\  of  §  =  ? 
Written  Work. 
1.    |  of  |  =  ? 

SOLUTION.  —  }  of  f  =  2  X  &  of  f . 

i  of  J  =  i. 
^§  of  |  =  2  X  i  =  | i  =  i- 

Rule.  — Keduce  integers  and  mixed  numbers  to  im- 
proper fractions.  Multiply  the  numerators  together  for  the 
numerator  of  the  product,  and  the  denominators  for  the 
denominator  of  the  product. 

Cancel  when  possible. 

Two  or  more  fractions  joined  by  (of)  form  a  Compound 
Fraction. 

The  word  of  is  equivalent  to  the  sign  of  multiplication. 

1.  Multiply  &  by  6.       5.    87  times  J§  =  ? 

2.  Multiply  ig  by  10.     6.   45  times  }f  =  ?    (Problem.) 

3.  Multiply  §{  by  17.     7.    35  times  ^  =  ? 

4.  Multiply  JJ  by  16.     8.    18  times  §f  =  ?    (Problem.) 
9.  Multiply  18|  by  8,  first  reducing  the  mixed  number 

to  an  improper  fraction. 

10.  Multiply  18f  by  8  without  reducing  the  mixed  num- 
ber to  an  improper  fraction.      First  multiply  the  fraction, 
then  the  integer,  by  8,  and  add  the  products.     Thus  : 

18J  SOLUTION.  — 

•      8  8  times  }  =  2?*  =  6 

6  8  times  18  =      144 

144  150 

150 

11.  16|  multiplied  by  10.        14.    Multiply  27|$  by  38. 

12.  126 1  multiplied  by  9.        15.    Multiply  35£f  by  46. 

13.  326£  multiplied  by  5.        16.    9  times  2}f  £  =  ? 


MULTIPLICATION   OF    FRACTIONS.  123 

17.  At  37  J  cents  a  pound,  what  will  16  Ib.  of  tea  cost  ? 

18.  Find  the  cost  of  17  barrels  of  flour  at  $7|  a  barrel  ? 

19.  |  of  160  =  ?  23.    Multiply  195  by  |f . 

20.  |  times  160  =  ?  24.    Multiply  326  by  f  J. 

21.  160  times  f  =  ?  25.    Multiply  584  by  -£%. 

22.  J  of  126  =  ?  26.    Multiply  1680  by  if. 

27.  Multiply  47  by  6}. 

47         SOLUTION.  —  f  of  47  =          14  J 

_6|  6  times  47  =  102 

14J  Il6|   Ans. 

102 

116J 

28.  Multiply  65  by  7f .  30.    4  J  times  48  =  ? 

29.  Multiply  125  by  14f .  31.    10/¥  times  385  =  ? 

32.  At  f  16  a  ton,  what  will  17}  tons  of  hay  cost  ? 
Multiply : 

33.  12|  by  30.  36.    24 Jf  by  48. 

34.  36T\  by  60.  (Problem.)     37.    28f  by  9.       (Problem.) 

35.  41f\by20.  38.    3269|by5.    (Problem.) 

39.  What  will  65}  bushels  of  potatoes  cost  at  40  cents  a 
bushel  ? 

40.  If  a  train  travels  58 £f  miles  in  one  hour,  how  far 
can  it  travel  in  24  hours  ? 

Find  the  product : 

41.  if  X  fV?        44-  J  X  i?  X  T\  47.  16|  X  6| 

42.  fo  x  11  45.  J j  X  J  X  6J  48.  5j  X  5j 

43.  25§  X  if        46.  5g  X  7J  X  4|  49.  §}  X  ff 

50.  What  is  the  cost  of  28|  yards  of  broadcloth  at  $2f 
a  yard  ? 

51.  What  is  the  cost  of  4}  cords  of  wood  at  $4}  a  cord  ? 


124  ARITHMETIC. 

Change  the  following  compound  fractions  to  simple 
fractions  : 

52.    $  of  T6T  of  ||  of  14.        53.    £  of  f  of  21-f  . 

54.  What  is  the  cost  of  35  Ib.  of  butter  at  37^  cents 
a  pound,  28  bushels  of  wheat  at  87£  cents  a  bushel,  and 
250  bushels  of  oats  at  22J-  cents  a  bushel  ? 

DIVISION  OF  FRACTIONS. 
Oral  Work. 
1.    J  is  contained  in  1  how  many  times  ? 

SOLUTION.  —  th?rd  is  contained  in  3  times. 


2.  §  is  contained  in  1  how  many  times  ? 

SOLUTION.  —  Since  £  is  contained  in  1  three  times,  §  is 
contained  in  1  one-half  as  many  times,  or  J  of  3  times, 
which  is  |  times.  Ans. 

3.  f  is  contained  in  $  how  many  times  ? 

SOLUTION.  —  §  is  contained  in  one  J  times.  It  is  con- 
tained in  £  just  £  as  many  times  as  it  is  in  1. 

Since  §  is  contained  £  times  in  1,  in  £  it  is  contained  J  of 
|  times,  which  is  f  times.  Ans. 

Thus  we  see  that  j  -f-  §  is  equivalent  to  f  multiplied  by  f  . 

4.  By  what  do  we  multiply  when  we  divide  by  |  ?     |  ? 

5?   i?  i?   4? 

5-    1-1  =  ?     i-f  =  ?      f-i=? 

6.  How  many  times  is  J  contained  in  1  ?  in  £  ?  in  §  ? 
in  J  ?  in  f  ? 

7.  Write  problems,  using  the  fractions  in  Ex.  5. 

8.  How  many  pens  can  be  bought  for  3  cents  if  one 
pen  costs  £  a  cent  ? 

9.  If  tea  costs  $|  a  pound,  how  much  tea  can  be  bought 
for  $1  ?  for  $1  ?  for  f  f  ? 


DIVISION   OF   FRACTIONS.  125 

Written  Work. 

NOTE.  —  To  divide  by  a  fraction  is  to  multiply  by  that 
fraction  inverted. 

Rule. 

Multiply  the  dividend  by  the  divisor  inverted. 
Reduce  integers  and  mixed  numbers  to  improper  factions, 
and  cancel  when  possible. 
Find  the  quotients : 

L      i-i-f  4.    |f  -2  7.    51-2J 

2.  H-s-f  5.    21  -f  8.    10 -f 

3.  y5¥  _i_  3  6.    16  -T-  4f  9.    5^  -^  8f 

f  -T-  }  may  be  written  |.     Such  an  expression  is  called  a 
Complex  Fraction,  and  is  used  simply  to  indicate  division. 

10.  Change  Examples  1  to  9  to  the  form  of  complex 
fractions. 

11.  Eead  each  of  them. 

A  Complex  Fraction  is  a  fraction  having  a  fraction  for  one 
or  both  of  its  terms. 

12.  Eead  the  following,  and  change  to  simple  fractions. 

4|  18|  |  10  4f 

2'  *'  r  t'  7f 

13.  22|  -^  7  =  ? 

SOLUTION.  —  7  is  contained  in  22|,  3  times,  with  a  re- 
7)22|      mainder  of  If  or  J  ;  this  divided  by  7  =  ^  or  J. 
3J      The  quotient  is  3J.      When  not  convenient  to  di- 
vide this  way,  proceed  according  to  rule.       Prove  by  other 
method. 

14.  16|  -  5  =  ?  16.    45?  ~  6  =  ?  (Problem.) 

15.  30f  -;-  7  =  ?  (Problem.)  17.    33J  ^  9  =  ? 

18.  264£  ^  4  =  ? 

19.  9826^  -T-  6  =  ?     (Problem.) 


126  ARITHMETIC. 

20.    17  -r-  4|  =  ? 

4§     17  This  may  be  divided  according  to  rule,  but 

3       _3       the  division  is  sometimes  shortened  as  follows  : 
14    )  51  Reduce  both  dividend  and  divisor  to  thirds. 

3A     4    =  and  17  =  J*  is  contained  in 


as  many  times  as  14  is  contained  in  51,  which  is  3^  times. 

21.  34  -f-  2g  =  ?     (Problem.)      24.        99  -r-  15J  =  ? 

22.  16  ^  5J  =  ?  25.    3694  -5-  2f    =  ? 

23.  126  -r-  3|  =  ?     (Problem.)      26.        85  -r-  4^  =  ? 

27.  If  16  bushels  of  apples  cost  $8|,   what  will  one 
bushel  cost  ? 

28.  A  sum  of  $2369  J  was  divided  equally  among  5  heirs. 
What  was  each  one's  share  ? 

29.  How  much  is  wheat  a  bushel  when  15  bushels  cost 


30.  When  |  of  a  pound  of  tea  costs  $$,  what  is  the  price 
per  pound  ? 

31.  The  product  of  two  numbers  is  16|.     One  of  the 
numbers  is  7.     What  is  the  other  ? 

32.  At  $1  per  yard,  how  many  yards  of  cloth  can  be 
purchased  for  $11  ? 

33.  In  how  many  days  can  a  horse  eat  6  bushels  of  oats, 
if  he  eats  |  of  a  bushel  a  day  ? 

34.  If  it  takes  2£  yd.  of  ribbon  to  trim  a  lady's  hat, 
how  many  hats  can  be  trimmed  with  10  yards  ? 

35.  If  4  apples  cost  6£  cents,  what  will  1  apple  cost  ? 
3  apples  ?  11  apples  ? 

36.  If  5  oranges  cost  16|  cents,  what  will  7  oranges  cost  ? 

37.  6    X  ?  =  14|  40.    5}|  X  ?  =    6 

38.  5|  X  ?  =    2J  41.    3i     X  ?  =  15J 

39.  31  X  ?  =  12  42.      §    X  ?  =    1J 


REVIEW.  127 

43.  If  |  of  an  acre  of  land  is  worth  $250,  what  is  1  acre 
worth  ? 

44.  What  will  5  doz.  eggs  cost,  when  f  of  a  dozen  cost 
15  cents  ? 

45.  At  $5  J  a  barrel,  how  many  barrels  of  flour  can  be 
bought  for  $75  ? 

Written  Work. 

Find  the  sum  : 

i.  i  +  i+i        «•*  +  *  +  *  +  ! 

2.  t  +  A  +  §  7-  J  +  f  +  t  +  £ 

3-  §  +  |  +  T5*  *    »  +  *  +  *  +  » 

4-  »  +  A  +  t  9'    £  +  t+T7s  +  § 

6-  !  +  «  +  §  10-  A  +  i  +  i  +  H 

11.    34|  12.    165J  13.    364| 


29H  284f 

19f 


Find  the  difference  and  prove  by  addition  : 

1.  i§  -  |  6.    15J  -  12/ff  11.    16f     -  llf 

2.  ||  -  }  7.    18J  -  16J  12.    28|      -  A 

3-    ft  -  J  8-    28^  -  13I  13-    184      - 

4.  £  —  J  9.    65|  —  18  J  14. 

5.  -3  10.    43  1  -  2890  15. 


Find  the  value  of  : 

I-    J  +  l-i  +  i  5.  4i 

2-?  +  J-t  +  *  6.  12|  -  5^  +  7  A 

3-    T4ir  +  T85  -  A  -  A  7.  6  +    4*  -  1|  + 

*•       --       +  8-  9-4T30-  +  3?- 


128  ARITHMETIC. 

PARTS   OF  A    DOLLAR. 
6J  cents  =  $TV  37£  cents  ==  $$ 

8£  cents  =  $T^  50    cents  =  $£ 

12|  cents  =  $J  62£  cents  =  $f 

16§  cents  =  $J  66|  cents  =  f  f 

25    cents  =  $£  75    cents  =  $J 

33J  cents  =  $£  87£  cents  =  f  J 

What  is  the  cost  of  33  books  at  16§/  each  ? 
33  books  cost  33  times  16§/,  or  33  times  $J  =  $ 
$5.50.     ^47i5. 
Oral  Work. 
Multiply : 

1.  12£  cents  by  16.  7.   37£  cents  by  8. 

2.  16|  cents  by  12.  8.    50    cents  by  15. 

3.  25    cents  by  20.  9.    62£  cents  by  8. 

4.  33£  cents  by  27.  10.    66|  cents  by  9. 

5.  6J  cents  by  16.  11.    75    cents  by  4. 

6.  8J  cents  by  24.  12.    87£  cents  by  8. 

13.  What  is  the  cost  of : 

16  Ib.  of  bacon  @  12£/  a  pound  ? 

16  balls  @  50/  each  ? 

36  yd.  of  ribbon  @  33J/  a  yard  ? 

36  Ib.  of  candy*  @  25/  a  pound  ? 

8  Ib.  of  tea  @  62£/  a  pound  ? 
Written  Work. 
Make  out  a  bill,  and  supply  place,  date,  and  names. 

14.  66  Ib.  of  pork  at  12£  cents  a  pound. 
48  Ib.  of  veal  at  16§  cents  a  pound. 

65  boxes  strawberries  at  25  cents  a  box. 
15  yd.  flannel  at  33^  cents  a  yard. 
80  Ib.  honey  at  25  cents  a  pound. 
48  Ib.  tea  at  50  cents  a  pound. 


PARTS    OF   A   DOLLAR. 


129 


1.  Find  the  cost  of  : 

16  Ib.  of  tea  @  62J/. 

2  yd.  flannel  @  66f /. 
84  gal.  molasses  @  75/. 
16  doz.  oranges  @  37  J/. 
50  Ib.  butter  @  25/. 

2.  At  25/  a  pound,  how  many  pounds  of  butter  can  be 
bought  for  $8  ? 

As  many  pounds  as  25/  or 
$8  -f-  $1  =  32  pounds.     Ans. 

Oral  Work. 

Divide  : 

3.  $3  by  33J/. 

4.  $5  by  25/. 

5.  $2  by  8J/. 

6.  $9byl2i/. 

7.  $1  by  6i/. 

13.  At  25  cents  apiece,  how  many  hats  can  be  bought  for 
$6? 

14.  At  25  cents  a  pound,  how  many  pounds  of  cheese 
can  be  bought  for  $5  ? 

15.  At  16|  cents  a  dozen,  how  many  dozen  eggs  can  be 
bought  for  $4  ? 

16.  How  many  pounds  of  beef  can  be  bought  for  $4,  at 
$.16|  a  pound  ? 

17.  At  33 \fl  a  yard,  how  many  yards  of  linen  can  be 
bought  for  $10  ? 

18.  How  many  penknives  can  be  bought  for  $6,  at  33J 
cents  apiece  ? 

19.  24  x  $.12^  =  ? 

20.  $24  ^-  $.12J  =  ? 


is  contained  times  in 


8.  f!0by50/. 

9.  $6  by  33J/. 

10.  $4byl2j/. 

11.  $2by25/. 

12.  $3  by 


130  ARITHMETIC. 

Written  Work. 

1.  At  $.75  a  bushel,  how  many  bushels  of  corn  can  be 
bought  for  $48  ? 

2.  At  62J/  a  bushel,  how  many  bushels  of  oats  can  be 
bought  for  $45  ? 

3.  At  66§  cents  each,  how  many  knives  can  be  bought 
for  $7J  ? 

4.  When  potatoes  are  25  cents  a  bushel,   how  many 
bushels  can  be  bought  for  $16  ? 

5.  When  butter  is  33J/  a  pound,  how  many  pounds  can 
be  bought  for  $68  ? 

6.  At  87J  cents  each,  how  many  arithmetics  can  be 
bought  for  $80  ? 

What  is  the  cost  of  : 

7.  6  doz.  lemons  at  37£  cents  a  dozen  ? 

8.  96  Ib.  of  candy  at  25/  a  pound  ? 

9.  356  pounds  of  butter  at  32J/  a  pound  ? 

10.  234  bu.  of  wheat  at  84|  cents  a  bushel  ? 

11.  46  yards  of  oil  cloth  at  36J  cents  a  yard  ? 

12.  96  doz.  eggs  at  16§/  a  dozen  ? 

13.  At  37J  cents  each,  how  many  articles  can  be  bought 
for  $80  ?  for  $63  ?  for  $33  ? 

14.  At  $|  a  day,  how  much  will  a  boy  earn  in  a  week  ? 
in  26  days  ?  in  300  days  ? 

15.  Make  out  two  bills,  using  fractional  parts  of  a  dollar 
for  prices.     Supply  names,  place,  date,  etc. 

Divide  : 

16.  $12i  by  25  cents.  20.  $18.33^  by  33J  cents. 

17.  $16.75  by  33J  cents.  21.  $15.89  by  12J  cents. 

18.  $14.53  by  16|  cents.  22.  $18.66f  by  33J  cents. 

19.  $65.14J  by  50  cents.  23.  $400.15  by  12J  cents. 


QUESTIONS   OF   RELATION.  131 

THE  THREE  QUESTIONS  OF  RELATION. 

(a)  3  X  4  =  12  ; 

(b)  therefore  12  •+-  4  =  3  ; 

(c)  and  12  -f-  3  =  4.. 

These  statements  placed  in  the  form  of  questions  would 
be  as  follows  : 

(a)  3  times  4  =  what  ?     Ans.  12. 

(b)  12  is  how  many  times  4  ?     Ans.  3  times. 

(c)  12  is  3  times  what  ?     Ans.  4. 

1.  Form  the  three  questions  from  the  following  state- 
ment, 5  X  6  =  30. 

Question  a.    %  of  8  equals  what  ?     Ans.  4. 

Question  b.    4  is  J  of  what  ?     Ans.  8. 

Question  c.    4  is  what  part  of  8  ?     Ans.  J. 

SOLUTION.  —  The  product  of  two  numbers  divided  by  one 
of  them  equals  the  other. 

Since  J  X  8  ==  4, 
then,  4  -f-  £  =  8, 
and,  4  -i-  8  =  £. 

2.  J  of  24  =  what  ? 

With  the  product  and  one  of  the  given  numbers,  form  a 
question  like  question  b ;  like  question  c. 

3.  16  is  4  of  what? 

SOLUTION.  —  It  is  evident  that  16  is  the  product  of  two 
numbers,  and  ^  is  one  of  them.  Therefore,  16  -=-  J  = 
48.  Ans. 

4.  What  part  of  48  is  16  ? 

SOLUTION.  —  It  is  evident  that  16  is  the  product  of  two 
numbers,  and  48  is  one  of  them.  Therefore,  16  -s-  48  =  J§ 
=  i,  Ans. 


132  ARITHMETIC. 

NOTE.  —  The  foregoing  treatment  of  this  class  of  ques- 
tions will  be  found  exceedingly  helpful  in  Percentage  and 
all  its  applications.  Each  of  these  three  typical  questions 
forms  the  basis  of  the  other  two.  When  one  of  these 
is  given,  the  pupils  should  be  required  to  give  both  the 
others  until  very  familiar  with  them,  and  when  a  problem 
is  found,  involving  one  of  the  Three  Questions,  pupils 
should  be  able  to  state  the  right  question  at  sight. 

When  the  pupil  can  state  the  question,  the  correct  solu- 
tion is  assured,  for  the  question  is  the  key  that  unlocks  the 
problem. 

Solve  each  of  the  following,  and  tell  whether  it  is  under 
question  a,  b,  or  c,  and  state  the  other  two  questions. 

Mental  Work. 

5.  |  of  12  is  what  ?  11.    4  is  J  of  what  ? 

6.  8  is  what  part  of  24  ?       12.    What  part  of  10  is  9  ? 

7.  What,  part  of  18  is  6  ?      13.    f  of  6  =  what  ? 

8.  15  is  |  of  what  ?  14.    9  is  £  of  what  ? 

9.  How  much  is  §  of  9  ?        15.    What  part  of  8  is  1  ? 
10.    What  part  of  9  is  3  ?        16.    4  is  what  part  of  5  ? 
Written  Work. 

To  THE  PUPIL. — Think  what  the  question  is  before 
attempting  to  solve  the  problem. 

17.  James  had  56  marbles,  and  John  f  as  many.     How 
many  had  John  ? 

18.  What  is  the  question  in  Example  17  ? 

19.  A  man  sold  f  of  his  farm,  and  had  50  acres  left. 
How  many  acres  were  there  in  the  entire  farm  ?     (Ques- 
tion.)    How  many  acres  did  he  sell  ?     (Question.) 

20.  A  boy  had  15  cents,  and  spent  6  cents  for  candy. 
What  part  of  his  money  did  he  spend  ?    (Question.)    What 
part  was  left  ?     (Question.) 


BEVIEW    OF   FRACTIONS.  133 

21.  What  is  the  cost  of  a  ton  of  hay,  when  f  of  a  ton  is 
worth  $9  ?     (Question.) 

22.  |  of  a  basket  of  eggs  were  sold  for  $6.24.     At  the 
same  price,  what  did  the  entire  basket  sell  for  ?  (Question.) 

23.  If  I  can  build  a  wall  in  8  days,  what  part  of  the  wall 
can  I  build  in  5  days  ?     (Question.) 

24.  James  spent  $12,  which  was  f  of  his  money.     How 
much  had  he  at  first  ?     How  much  had  he  left  ? 

25.  In  my  pasture  are  49  sheep,  which  is  T75  of  my  entire 
flock.     How  many  sheep  have  I  ?     (Question.) 

What  part  of  my  sheep  were  not  in  the  pasture  ? 
How  many  sheep  were  not  in  the  pasture  ? 

26.  John  runs  360  yards,  and  Henry  £  as  far.     How  far 
does  Henry  run  ?     (Question.) 

27.  Henry  ran  300  yards,  which  is  $  as  far  as  John  ran. 
How  far  did  John  run  ?     (Question.) 

28.  If   Dick   has    $5    and   Eobert   #15,   what   part   of 
Robert's   money  is    Dick's  ?     (Question.)     What  fraction 
of  Dick's  is  Robert's  ?     (Question.) 

29.  If   a  barrel  can  be  filled  by  a  pipe  in  40  minutes, 
what  part  of  it  can  be  filled  in  35  minutes  ?     (Question.) 

30.  What  part  of  15  is  8  ?     (Problem.) 

31.  50  is  what  part  of  150  ?     (Problem.) 

32.  50  is  |  of  what  ?     (Problem.) 

33.  What  is  VV  of  34°  ?     (Problem.) 

34.  What  part  of  §  is  f  ? 

35.  What  part  of  f  is  J  ? 

REVIEW   OF  FRACTIONS. 
Written  Work. 


134  ARITHMETIC. 

2.  Reduce  to  lowest  terms :  ||  ; 

3.  Eeduce  to  integers  or  fractions :  8T\  ;  9f  ;  15J. 

4.  Reduce  to  mixed  numbers  :  f  j  ;  ^  ;  ^  ;  *?f&. 

5-    f  +  f  =  ?       A  +  M  +  41  =  ? 

6.  6|  +  7  A  =  ?     29J  +  17§  =  ? 

7.  Add :  206|,  509T%,  1056|,  109TV 

a  I  - 1  -  ?    f  -  t\  =  ?    ii  -  }  =  ?    I  -  A  = 

9.  142  _  14J  =  ?  17J  -  15|  =  ?  183  -  124f  =  ? 

10.  j  of  16  =  ?  5§  x  11  =  ?  f  X  i  XJi  X  }f 

11.  2064  X  3}  =  ?     2693f  X  4  =  ?      2j  x  4§  x 
3J  =  ? 

12.  J  -5-  6  =  ?     g^4  =  ?     ^T^-9  =  ?     }|  ^-  6  =  ? 

13.  16  -f-  5  =  ?     14  -f-  i  =  ?     15  ^-  J  =  ? 

14.  216|  -  5  =  ?     3046g  -4-  2  =  ?     321^  ^  18  =  ? 

15.  5  _,.  3  =  ?    3  j.  ^  =  ?    3}  -j-  2|  =  ?    42  -r-  5J  =  ? 

16.  Find   the   cost  of   four  pieces  of   cloth,  measuring 
23£  yd.,  25|  yd.,  22J  yd.,  and  21J  yd.,  at  $2  a  yard  ? 

17.  Charles  has   $15|  in  the  bank.     How  much  more 
must  he  earn  before  he  has  $50  ? 

18.  From  the  sum  of  2J  and  31J,  take  the  difference  of 
5J  and  4J.     (Indicate.) 

19.  Which  is  greater,  the  product  of  |  and  J,  or  the  dif- 
ference ?     How  much  ? 

20.  How  many  inches  in  j  of  a  yard  ?     (Question.) 

21.  A  man  drew  from  the  bank  $68,  which  was  |  of  his 
entire  deposit.     How  much  had  he  at  first  ?     (Question.) 

22.  A  sum  of   money  was  divided  between   John   and 
James.     John  received  f  of  it,  and  James  $300.     How 
much  did  John  receive  ? 

23.  A  merchant  paid   $272  for  flour,  at  $9f  a  barrel. 
How  many  barrels  did  he  buy  ? 


REVIEW   OF   FRACTIONS.  135 

24.  Subtract  2  from  both  terms  of  the  fraction  J.     Do 
you  increase   or  diminish  the  fraction,  and  how  much  ? 
Add  2  to  each  term,  and  find  the  difference. 

25.  What  must  be  added  to  f  +  If  +  J  to  make  5  ? 

26.  What  number  multiplied  by  25  J  will  make  264  ? 

27.  A  lady  gave   $J  for  ribbon,   $1   for  pins,   $|   for 
velvet,  and  $-J  for  lining.     What  change  did  she  receive 
from  a  five-dollar  bill  ? 

28.  What  will  4|  Ib.  of  raisins  cost,  at  15/  a  pound  ? 

29.  From  25  yd.  of  cloth,  a  tailor  used  If  yd.  for  making 
a  vest,  2£  yd.  for  a  pair  of  pantaloons,  3£  yd.  for  a  coat, 
and  4J  yd.  for  an  overcoat.     How  much  cloth  was  left  ? 

30.  I  owned  }  of  a  farm  and  sold  £  of  my  share.     What 
part  of  the  farm  did  I  sell,  and  what  part  did  I  retain  ? 

31.  How  many  rods  in  3642  feet  ? 

32.  If  4  quarts  of  grain  are  given  for  grinding  a  bushel, 
what  part  is  the  cost  for  grinding  ?     (Question.) 

33.  Henry  had  $78  in  the  bank.     He  withdrew  $15  at 
one  time  and  $38   at  another  time.     What  part  of   his 
money   did   he   withdraw  ?      (Question.)     What   part    re- 
mained ?     (Question.) 

34.  A  man  having  150  sheep  sold  §  of  them  and  kept 
the  remainder.     How  many  were  sold  ?     How  many  were 
kept? 

35.  A  man  owning  $  of  a  factory  sold  §  of  his  share. 
What  part  of  the  factory  did  he  sell  ? 

36.  What   part   of   6   bushels    1    peck   is   4   bushels  2 
pecks  ? 

37.  A  man  sold  50  sheep,  which  was  f  of  his  whole  flock. 
How  many  sheep  had  he  at  first  ? 

38.  At  $4|  a  yard,  what  will  5  yards  of  velvet  cost  ? 


136  ARITHMETIC. 

39.  4  yards  of  ribbon  cost  35£/;  what  was  the  price  per 
yard  ? 

40.  At  $3£  a  ream,  what  will  £  of  a  ream  of  paper 
cost? 

41.  If  20f  Ib.  of  sugar  cost  80  cents,  what  will  50  Ib. 
cost  ?     (Use  cancellation.) 

42.  If  20|  Ib.  of  sugar  cost  80/,  how  many  pounds  can 
be  bought  for  $2.00  ? 

43.  I  bought  55  yd.  of  cloth  at  $g  a  yard,  and  sold  it  at 
$f  a  yard.     What  was  the  profit  ? 

44.  If  an  acre  of  land  is  worth  $150,  what  part  of  an 
acre  will  $50  buy  ? 

45.  If  a  teacup  holds  J  of  a  pint,  how  many  cupfuls  in  a 
quart  ?     A  gallon  ? 

46.  If  |  of  my  money  is  $93,  how  much  is  |  of  it  ?    (1st 
Question.)     (2d  Question.) 

47.  You  sell  to  John  Grouse  the  following  goods : 

48  Ib.  of  butter  @  29£/. 
24J  Ib.  of  coffee  @  45/. 

gal.  of  oil  @  12|/. 

Ib.  of  tea  @  37|/. 

Make  out  a  bill  and  receipt  it. 

48.  How  many  feet  of  wire  will  be  required  to  fence  a 
lot  145J  ft.  deep,  and  having  55^  ft.  front,  the  fence  being 
four  wires  high  ?     (Illustrate.) 

49.  How  long  will  it  take  a  boy  to  pay  for  a  $75  bicycle, 
if  he  can  pay  $f  a  day  ? 

50.  f  of   a  class  are  boys ;    there  are  30  girls.      How 
many  pupils  in  the  class  ? 

51.  If   2|  Ib.  of  tea  cost  $1.00,  how  much  will  3J  Ib. 
cost? 


REVIEW   OF   FRACTIONS.  137 

52.  From  a  hogshead  of    molasses  ^  leaked  out;   what 
part  of  the  molasses  remained  ?     (Question.)     How  many 
gallons  remained  ? 

53.  At  $1  a  pound,  what  is  the  cost  of  %  pound  of  tea  ? 

54.  Find  the  product  of  §,  f ,  5f ,  and  2£. 

55.  From  369  take  25f . 

56.  Find  the  sum  of  £  of  44,  }  of  16,  and  j  of  24. 

57.  Find  the  product  of  J,  £,  £f ,  and  |. 

58.  What  is  a  compound  fraction  ? 

59.  A  paymaster  pays  each  of  his  men  $*.     How  much 
does  he  pay  22  men  ? 

60.  If  a  press  can  print  T5r  of  a  paper  in  a  second,  how 
many  papers  can  it  turn  out  in  a  minute  ? 

61.  If  the  fare  for  a  ride  on  the  steamer  Ontario  is  $$, 
what  will  it  cost  21  persons  to  take  the  ride  ? 

62.  A  family  eat  2£  Ib.  of  meat  a  day.     How  much  meat 
will  they  eat  in  a  week  ? 

63.  The  distance  from  Harry's  home  to  school  is  j  of  a 
mile.     How  many  miles  does  he  walk  in  a  week  in  going 
to  and  from  school  ? 

64.  Each  person  at  a  church  contributed,  on  an  average, 
$g.     There   were   295   persons   present.     What   was   the 
amount  of  the  collection  ? 

65.  If  Mary  can  pick  4§  quarts  of  berries  a  day,  how 
many  quarts  can  she  pick  in  a  week  ? 

66.  Mr.  Lynn,  the  shoemaker,  charges  $§•  for  making  a 
pair  of   shoes.     How  much  will   he   charge   for   making 
a  dozen  pair  ? 

Indicate  and  cancel : 

1.    What  is  the  value  of  J   of  my  lot,  if  T7^  of  it  is 
worth  $84  ? 


138  ARITHMETIC. 

2.  If  3£  yards  of  cloth  are  worth  $5f,  what  are  5| 
yards  worth  ? 

3.  If   3  bushels  of  grain  are  worth  $4|,   how  many 
bushels  can  I  buy  for  $26  ? 

4.  How  many  pounds  of  coffee  at  37J/  a  pound  can  be 
bought  for  $24f  ? 

5.  If  3  boxes  of  lemons  cost  $6|,  what  will  32  boxes 
cost? 

6.  If  3  boxes  of  oranges  can  be  bought  for  $6J,  how 
many  boxes  can  be  bought  for  $72  ? 

7.  A  boy  earned  $5j  at  the  rate  of  37£/  a  day.     How 
many  days  did  he  work  ? 

8.  7  cords  of  wood  at  $4£  a  cord  will  pay  for  how 
many  tons  of  coal  at  $3£  a  ton  ? 

9.  |  of  a  ton  of  coal  at  $4£  a  ton  will  pay  for  what 
part  of  a  cord  of  wood  at  $5  a  cord  ? 

10.  How  many  peaches  at  !£/  each  can  be  exchanged 
for  50  apples  at  £  cent  each  ? 

11.  J  is  what  part  of  f  of  f  ? 

12.  |  is  f  of  what  number  ? 

13.  The  product  of  two  numbers  is  2| ;  one  of  them  is 
f .     What  is  the  other  ? 

SQUARE   MEASURE. 

An  Angle  is  the  difference  in  direction  of  two  lines  that 
meet.  (Illustrate.) 

A  Right  Angle  is  the  angle  of  a  Square.     (Illustrate.) 

A  Surface  is  that  which  has  length  and  breadth,  but  not 
thickness,  as  a  page  in  a  book,  the  top  of  a  table. 

A  Rectangle  is  a  surface  having  four  sides  and  four  right 
angles. 

A  Square  is  a  rectangle  having  equal  sides. 


SQUARE    MEASURE. 


139 


Draw  two  different  kinds  of  rectangles,  and  tell  their 
difference. 

Point  out  some  surfaces  in  your  room  that  are  rectangles, 
and  not  squares. 

Are  there  any  perfect  squares  in  the  room  ? 

A  square  inch  is  a  square,  1  inch  long  and  1  inch  wide. 

Draw  a  square  inch. 

A  square  foot  is  a  square,  1  foot  long  and  1  foot  wide. 

Draw  a  square  foot  upon  the  blackboard.  See  that  the 
sides  are  exactly  1  foot  long,  and  the  angles  right  angles. 
What  is  a  square  yard  ?  Illustrate  upon  the  blackboard. 
Separate  it  into  square  feet.  What  is  a  square  rod  ?  Let 
two  pupils  come  early  in  the  morning  and  mark  off  a  square 
rod  on  the  floor,  and  let  others  measure  and  see  if  it  is 
correct. 

What  is  a  Square  Mile  ? 

The  Area  of  a  surface  is  the  number  of  square  units  that 
it  contains. 

What  is  the  square 
unit  in  this  figure  ? 

How  many  square 
inches  in  it  ? 

SOLUTION.  -  -  There 
are  six  square  inches 
in  a  row,  and  there  are 
4  rows,  therefore  4 
times  6  square  inches  =  24  sq.  inches.  Ans. 

NOTE.  —  In  finding  areas,  as  in  all  multiplication,  the 
multiplier  is  abstract,  and  the  unit  of  the  product  must  be 
the  same  as  the  unit  of  the  multiplicand. 

Oral  Work. 

1.  How  many  square  feet  in  a  surface  6  ft.  long  and  1 
ft.  wide  ? 


6  IN. 


140  ARITHMETIC. 

2.  In  a  surface  6  ft.  long  and  2  ft.  wide  ?     (Illustrate.) 

3.  How  many  square  feet  in  a  platform  5  ft.  long  and 
4  ft.  wide.     (Illustrate.) 

4.  What  is  the  area  of  a  mirror  3  ft.  long  and  2  ft.  wide  ? 

5.  Draw  a  rectangle  4  inches  long  by  2  inches  wide,  and 
divide  it  into  square  inches. 

6.  Draw  a  2-inch  square  and  divide  it  into  square  inches. 

7.  What  is  the  difference  between  a  2-inch  square  and 
2  square  inches  ?     (Illustrate.) 

8.  How  many  square  feet  does  a  5-foot  square  contain  ? 
Show  the  difference  between  a  5-f t.  square  and  5  square  feet. 

9.  If  the  top  of  a  table  is  5  ft.  long  and  4  ft.  wide,  what 
is  its  area  ? 

10.  If  the  area  of  a  floor  is  20  square  yards,  and  the 
length  5  yards,  what  is  the  width  ? 

The  length  and  breadth  of  a  rectangle  are  called  its 
Dimensions. 

Principle  1.  —  Area  is  the  product  of  length  multiplied 
by  breadth.  The  numbers  representing  length  and  breadth 
must  be  like  numbers. 

Principle  2. — Area  divided  by  either  dimension  gives 
the  other. 

11.  Give   a    problem,    to   find   area,    when    length   and 
breadth  are  known. 

12.  From  that  problem  give  another,  to  find  length,  when 
area  and  width  are  known. 

13.  Give  another,  to  find  width,  when  area  and  length 
are  known. 

14.  How  long  is  a  path  whose  area  is  48  square  feet,  and 
whose  width  is  4  feet  ? 

15.  How  wide  is  a  pavement  that  contains  56  sq.  yards 
and  is  8  yards  long  ? 


SQUARE   MEASURE.  141 

TABLE. 

144    square  inches  =  1  square  foot  (sq.  ft.) 

9    square  feet      =  1  square  yard  (sq.  yd.) 
30i  square  yards    =  1  square  rod  (sq.  rd.) 
160    square  rods      =  1  acre  (A.) 
640    acres  =  1  square  mile  or  section  (sq.  mi.,  sec.) 
Written  Work. 

1.  How  many  square  inches  in  3  sq.  feet  ? 

2.  How  many  square  yards  in  54  sq.  feet  ? 

3.  In  12^  sq.  ft.  how  many  sq.  inches  ? 

4.  How  many  acres  in  480  square  rods  ? 

5.  In  7212  sq.  in.,  how  many  sq.  feet  ? 
Reduce  to  square  inches  : 

6.  4  sq.  ft.  15  sq.  in.  7.    8  sq.  ft.  110  sq.  in. 

8.  2  sq.  yd.  4  sq.  ft.  78  sq.  in. 

9.  25  sq.  yd.  6  sq.  ft.  12.    2£  sq.  ft. 

10.  6  sq.  yd.  12  sq.  in.  13.    J  sq.  yd. 

11.  5J  sq.  yd.  14.    £  sq.  yd.  £  sq.  ft. 

15.  1  sq.  rd.  1  sq.  yd.  1  sq.  ft.  1  sq.  in. 
Reduce  to  higher  denominations  : 

16.  5680  sq.  in.  19.    7200  sq.  in. 

17.  38204  sq.  in.  20.    450  sq.  rd. 

18.  3296  sq.  in.  21.    264321  sq.  ft. 

22.  In  30  A.  14  sq.  rd.  how  many  square  rods  ? 

23.  Reduce  34232  sq.  rods  to  higher  denominations. 

24.  Reduce  14  sq.  rd.  18  sq.  yd.  15  sq.  ft.  82  sq.  in.  to 
inches. 

25.  What  part  of  a  sq.  yard  is  a  sq.  ft.  ?     (Question.) 

26.  2  sq.  ft.  is  what  part  of  2  sq.  yd.  ?     (Question.) 

27.  Reduce  120  sq.  rd.  4  sq.  yd.  to  sq.  yards. 


142  ARITHMETIC. 

28.  In  40  acres,  how  many  square  rods  ?  square  yards  ? 

29.  In  £  of  an  acre  how  many  sq.  rods  ?  sq.  yards  ? 

30.  How  many  square  feet  in  the  top  of  a  table  5£  ft. 
long  and  four  feet  wide  ?     How  many  square  inches  ? 

31.  What  is  the  area  of  a  basement  36  ft.  by  18^  ft.  ? 

32.  At  22/  a  square  foot,  what  is  the  cost  of  a  flag  walk 
50  ft.  X  6  ft,  ? 

33.  How  wide  is  a  floor  whose  area  is  300  sq.  ft.,  and 
whose  length  is  20  ft.  ? 

34.  5  flag-stones,  each  5£  ft.  by  6  ft.,  will   cover  how 
much  surface  ? 

35.  In  a  room  are  4  doors,  each  7  ft.  6  in.  by  2  ft.  8  in. 
How  many  square  feet  in  the  surface  of  the  four  doors  ? 
How  many  square  inches  ? 

36.  A  pasture  containing  4  acres  is  20  rods  wide.     How 
long  is  it? 

37.  A  city  lob  containing  8400  sq.  ft.  is  140  ft.  deep. 
What  is  the  frontage  ?     (Illustrate.) 

38.  How  many  acres  in  a  field  £  mile  square  ? 

39.  Is  there  any  difference  between  a  mile  square  and  a 
square  mile  ?     (Illustrate.) 

40.  A  farmer  had  a  section  of  land.     He  sold  £  of  it  to 
one  man  and  J  to  another.     How  many  acres  had  he  left  ? 
What  part  of  the  farm  is  left  ? 

41.  How  many   sq.   yards   in  a   ceiling   that   is   15  ft. 
square.     (Illustrate.) 

42.  From  |  of  a  sq.  mile  of  land,  I  sold  a  farm  80  rods 
long  by  40  rods  wide.     How  many  acres  have  I  left  ? 

43.  A  garden  is  300  ft.  long  and  200   ft.  wide.     How 
many  flower-beds  in  J  of  it,  if  each  bed  covers  100  sq.  ft.  ? 

44.  How  many  square  rods  in  a  field  20  rods  square  ? 


SQUARE   MEASURE.  143 

45.  How  many  square  yards  of  carpeting  will  cover  a 
floor  5  yd.  long  and  4  yd.  wide  ? 

46.  A  school  yard  of  120  sq.  rods  is  8  rods  wide.     How 
long  is  it  ? 

47.  How  many  square  inches  in  a  board  15  ft.  long  and 
12  inches  wide  ?     (Illustrate.) 

48.  A  field  160  by  50  rods  contains  how  many  acres  ? 

49.  How  many  square  yards  in  a  strip  of   wall  paper 
28  yd.  long  and  2  ft.  wide  ? 

60.    How  many  square  feet  of  boards  will  it  take  to  make 
a  tight  board  fence  150  ft.  long  and  4|  ft.  high  ?  t 

51.  How  many  3-inch  squares  can  be  cut  from  a  strip  of 
pasteboard  3  ft.  long  and  18  inches  wide  ? 

52.  A  blackboard  is  16  ft.  long  and   4  ft.  4  in.  wide. 
What  is  its  area  in  square  feet  ? 

53.  How  many  inch  squares  in  a  piece  of  paper  10  X  8 
inches  ?     How  many  half-inch  squares  ? 

54.  At  4/  a  sq.  ft.,  how  much  will  10  cherry  boards  cost, 
each  board  being  12  ft.  long  and  1  ft.  3  in.  wide  ? 

55.  How  many  square  feet  in  a  roof  that  is  30  ft.  long 
and  20  ft.  wide  on  each  of  the  two  sides  ? 

56.  How  many  rods  long  must  a  pasture  be  that  is  20  rd. 
wide  to  contain  2  acres  ? 

57.  The  floor  of  a  bedroom  is  9  feet  wide,  and  is  cov- 
ered by  12  sq.  yards  of  carpet.     How  long  is  it  ? 

58.  What  will  be  the  cost  of  16  feet  of  wire  cable  at 
12  £/  a  foot  ?  t 

69.    How  many  blocks  3  inches  square  can  be  cut  from  a 
board  9  X  12  inches  ? 

60.  Eeduce  1  sq.  rod  to  square  feet. 

61.  Eeduce  2798  sq.  inches  to  higher  denominations. 


144  ARITHMETIC. 

SHORT  MULTIPLICATION. 

To  multiply  when  the  unit  figure  of  the  multiplier  is  1. 

3825  X  31     Multiply  by  3,  write  the  product  under 
11475  the  multiplicand  one   place  to  the  left, 

118575  and  add. 

Multiply  and  prove  : 

1.  6984  X  51  4.   2863  x     71 

2.  3584  x  21  5.      564  x  HI 

3.  5832  X  41  6.    2852  x  121 
A\%en  the  tens  figure  of  the  multiplier  is  1. 

3862  x  15     Multiply  by  5,  write  the  product  under  the 
19310  multiplicand  one   place   to   the  right,   and 

57930  add. 

Multiply  and  prove  : 

7.  2836  X  14  11.    2864  x  12 

8.  38987  X  17  12.    3984  X  13 

9.  2863  x  18  13.   3549  X  19 
10.      3684  x  16  14.      896  X  15 

15.  At  $21  a  ton,  what  is  the  cost  of  285  tons  of  hay  ? 

16.  At   18   cents  each,  what  will   be  the  cost  of   286 
blank  books  ? 

17.  How  far  can  a  train  run  in  648  hours  at  the  rate  of 
51  miles  an  hour  ? 

18.  A  wholesale  grocer  purchased   3984  dozen  eggs  at 
a  dozen.     What  was  the  cost  ? 


19.  If   a  common  soldier  receives    $14   a  month,  what 
must  be  paid  2856  soldiers  for  one  month's  service  ? 

20.  At  $31  a  head,  what  will  be  the  cost  of  356  cattle  ? 

21.  384  x  18  X  41  =  ? 


PABTS   OF    100  AND    1000.  145 

PARTS  OF  100  AND  1000. 

Written  Work.  —  Short  Multiplication. 

1.  What  part  of  100  is  12J  ?     25  ?     33|  ? 

2.  What  part  of  1000  is  125  ?     250  ?     333£  ? 

3.  How  much  is  1  of  100  ?     \  of  1000  ? 

4.  How  much  is  £  of  100  ?     J  of  1000  ? 

5.  How  much  is  £  of  100  ?     J  of  1000  ? 

6.  25  times  24  =  ? 

EXPLANATION.  —  25  times  24  is  J  as  much  as  100  times 
24.     1-00  times  24  is  2400.     \  of  2400  is  600.     Ans. 

To  multiply  by  25,  annex  two  naughts,  and  take  one- 
fourth  of  the  result. 

7.  Tell  how  to  multiply  by  12£,  33J,  125,  250,  333J. 

8.  Multiply  first  by  25,  then  by  250 :  8,  20,  28,  72,  96, 
248,  1696. 

9.  Multiply  first  by  12£,  then  by  125 :  16,  24,  48,  96, 
144,  264,  1448. 

Rapid  Work,  Without  Pencil. 


10. 

56 

X 

25 

15. 

25 

X 

444 

20. 

42 

X 

33J 

11. 

12* 

X 

32 

16. 

25 

X 

368 

21. 

80 

X 

12i 

12. 

36 

X 

33J 

17. 

33J 

X 

993 

22. 

25 

X 

68 

13. 

96 

X 

12* 

18. 

33J 

X 

846 

23. 

76 

X 

25 

14. 

168 

X 

12i 

19. 

72 

X 

12* 

24. 

168 

X 

12* 

Written  Work. 

25.  250  x  44  29.  333 J  X  42  33.  1863  X  333 J 

26.  27  X  333^  30.  250  X  648  34.  250  X  7676 

27.  125  X  168  31.  125  X  648  35.  125  X  1672 

28.  125  X  64  32.  426  X  333  J  36.  9684  X  250 


146  ARITHMETIC. 

Oral  Review 

1.  If  5  bbl.  of  flour  cost  $25,  what  will  8  bbl.  cost  ? 

2.  If  5  bbl.  of  flour  cost  $25,  how  many  barrels  can  be 
bought  for  $60  ? 

3.  How  many  inches  long  is  a  10-foot  pole  ? 

4.  What  is  the  cost  of  2  doz.  lead  pencils  at  4/  each  ? 

5.  What  is  T\  of  84  ? 

6.  What  will  5  oranges  cost,  if  a  dozen  cost  36  cents  ? 

7.  What  number  added  to  4  £  will  equal  9£  ? 

8.  A  boy  had  48  marbles.     He  lost  8  in  the  morning,  7 
at  recess,  and  6  at  noon.     In  the  afternoon  he  found  7  and 
bought  12  new  ones.     How  many  marbles  had  he  at  the 
close  of  the  day  ? 

9.  If  4  men  can  do  a  piece  of  work  in  9  days,  in  how 
many  days  can  6  men  do  it  ? 

10.  If  a  boy  can  earn  $30  in  6  weeks,  how  much  can  he 
earn  in  10  weeks  ? 

11.  What  are  the  prime  factors  of  48,  72,  and  96  ? 

12.  In  }  of  an  apple  how  many  eighths  ? 

13.  Which  is  larger,  £  or  |,  and  how  much  ? 

14.  ^  is  how  many  times  ^  ? 

15.  What  is  the  difference  between  £  and  £  ? 

16.  If  one  man  eats  §  Ib.  of  meat  at  a  meal,  how  many 
pounds  will  12  men  eat  ? 

17.  If  a  barrel  of  apples  cost  $2  J,  what  will  4  bbl.  cost  ? 

18.  How  much  is  4  times  5^  ? 

19.  If  a  barrel  of  flour  costs  $5J,  what  will  6  barrels 
cost? 

20.  2i  is  £  of  what  number  ? 

21.  3f  is  £  of  what  number  ? 


MISCELLANEOUS    REVIEW.  147 

Write  in  figures  : 

1.  Two  hundred  ninety-six  thousand,  forty. 

2.  Three  million,  three  thousand,  three. 

3.  Two  hundred  six  million,  five  hundred  five  thousand. 

4.  One  hundred  million,  one  hundred  thousand,  one. 

5.  Eight  million,  eight. 

6.  Write  the  smallest  number  that  can  be  written  with 
six  figures.     The  largest. 

7.  In  reading  numbers,  what  name  is  given  to  the  first 
right  hand  group  ?  the  second  ?  the  third  ? 

8.  What  number  is  made  up  of  eight  8's  written  hori- 
zontally ? 

Counting  from  the  right,  what  is  the  value  of  the  sec- 
ond 8  ?  the  fourth  8  ?  the  seventh  8  ? 

Add  these  three  values,  and  express  their  sum  in  words. 

9.  What  is  the  simple  value  of  any  figure  ?     The  local 
value  ? 

Write  in  figures  : 

10.  Five  hundred  fifty-five  million,  five  hundred  fifty-five 
thousand,  five  hundred  fifty-five. 

11.  Two  hundred  million,  two  hundred  thousand,  two. 
Eead  the  following : 

12.  206,391,401  18.    350,053,350 

13.  960,004,003  19.    999,999,999 

14.  11,311,114  20.    298,432,624 

15.  239,239,239  21.      83,083,083 

16.  1,001,001  22.       8,000,008 

17.  21,000,021  23.    316,048,006 


148  ARITHMETIC. 

Add: 


4,329 

2.  216,824 

3.  16,826 

26,263 

315,962 

194,295 

34,046 

16,822 

999,999 

99,004 

1,981 

698,423 

21,982 

124,306 

482,394 

821,366 

281,016 

100,004 

98,989 

192,498 

216,429 

26,032 

29,260 

918,492 

98,482 

234,234 

215,498 

132,014 

16,215 

888,888 

4.  Subtract  the  1st  sum  from  the  3d  sum  in  the  above 
examples. 

5-  If  a  clerk  earns  $1000  a  year,  how  much  will  he 
have  left  after  paying  his  board  at  the  rate  of  $20  a  month  ? 

6.  How  much  will  a  girl  spend  for  car  fare  in  a  year,  if 
she  pays  two  fares  every  day  except  Sundays  ? 

Multiply  : 

7.  8926  8.    58231  9.   46829  10.    99849 

298  8753  389  7689 

11.  What  is  the  sum  of  the  four  products  in  the  above 
examples  ?     The  four  multipliers  ? 

12.  Subtract  the  sum  of  the  multipliers  from  the  sum  of 
the  multiplicands. 

Add,  without  copying : 

13.   $    742,155.74  14.    $8,362.04 

429.39  36.09 

6,873.68  2,040.03 

397.49  295.98 

1,956,374.20  3,699.84 

284,326.19  1,582.67 


MISCELLANEOUS.  149 

Multiply  without  copying : 

1.    580092                      2.    698468                     3.    6940059 
9  8  7 

Subtract  without  copying : 

4.      28796  5.      36095  6.   From  361181 

from  398162  from  263069  29999 

7.  Divide  without  copying  : 

86929  by  8  ;  by  9  ;  by  10  ;  by  11 ;  by  12. 

8.  The  multiplicand  is  3894,  the  multiplier  12.     What 
is  the  product  ?     Prove  in  two  ways. 

9.  The  dividend  is  98486,  the  divisor  94,  what  is  the 
quotient  ?     Prove. 

10.  The  dividend  is  3846,  the  divisor  34,  the  quotient 
113,  and  the  remainder  14.     Prove. 

11.  The  divisor  is  171,  the  quotient  22,  and  the  remainder 
,  80.     What  is  the  dividend  ? 

12.  The  multiplier  is  396,  and  the  product  is  5148,  what 
is  the  multiplicand  ? 

13.  The  minuend  is  9842,  the  subtrahend  2989.     What 
is  the  difference  ?     Prove. 

14.  The  subtrahend  is  2869,  the  remainder  86594.     What 
is  the  minuend  ? 

15.  The  minuend  is  64682,  the  remainder  64497.     What 
is  the  subtrahend  ? 

Which  is  the  greater,  and  how  much  ? 

16.  48  X  364  or  63  X  295. 

17.  8694  -  356  or  3695  +  4782. 

18.  8695  —  16  or  1000  -  555. 

19.  Write  in  Roman,  36,984 ;  28,695  ;  186,005. 

20.  189763-4-329. 

21.  286976  -f-  57. 


150  ARITHMETIC. 

Indicated  Work. 

Indicate,  and  solve  by  cancellation  : 

1.  How  many  boxes,  each  holding  £  of  a  quart,  can  be 
filled  from  16  quarts  of  berries  ? 

2.  How  many  books  at  f  |  apiece  can  be  bought  for  $12  ? 

3.  If  a  man  earn  f  of  a  dollar  an  hour,  in  how  many 
hours  can  he  earn  $  15  ? 

4.  A  laborer  can  build  a  wall  -f?  of  a  rod  long  in  an 
hour.     How  many  such  walls  can  he  build  in  3£  days  of 
10  hours  each  ? 

5.    At  $  I  a  yard,  how  many  yards  of  cloth  can  be  bought 
for 


Parts  of  a  Dollar. 

1.  If  coffee  is  worth  25/  a  pound,  what  will  be  the  cost 
of  3  J  pounds  ? 

2.  When  tea  is  worth  37£/  a  pound,  how  much  tea  can 
be  bought  for  f  of  a  dollar  ? 

3.  At  f  |  a  pound,  what  will  2  Ib.  of  tea  cost  ? 

4.  How  many  books  can  be  bought  for  $3f,  when  one 
book  can  be  bought  for  62£  cents  ? 

5.  At  12  JX  a  quart,  how  many  quarts  of  berries  can  be 
bought  for  $16f  ? 

Add,  without  copying  : 

6.  36984  7.    $  384.62  8. 

2683  29.36 

95426  2943.99 

943  269.46 

29  98.43 

354  269.62 

2983  8936.15 

362  26.18 

513  827.25 


MISCELLANEOUS.  151 

1.  A  man  divided  his  estate  worth  $  8694  equally  among 
his  5  children.     How  much  did  each  receive  ? 

2.  The  salary  of  the  President  of  the  United  States  is 
$50,000  a  year.     How  much  is  that  a  day  ? 

3.  How  many  yards  of  linen  at  25/  a  yard,  must  be 
given  for  35  bushels  of  potatoes  at  50/  a  bushel  ?     Solve 
by  cancellation. 

4.  If  10  men  earn  $2600  in  a  month,  how  much  can  28 
men  earn  in  the  same  time  ? 

5.  A  man  earns  $50  a  week  and  spends  $29  a  week ; 
what  can  he  save  in  20  weeks  ? 

6.  I  bought  50  sheep  for  $200,  but  10  of  them  died. 
At  what  price  must  I  sell  each  of  the  rest  so  as  to  lose 
no  money  ? 

7.  What  must  I  ask  apiece  in  order  to  gain  $40  on  the 
sheep  that  are  left  ? 

8.  From  the  sum  of  $684.96  and  $283.94,  take  their 
difference. 

9.  How  many  2-foot  steps  will  a  boy  take  in  walking 
around  a  square  lot  140  feet  on  a  side  ? 

10.  Find  the  cost  of  a  horse  at  $250,  a  carriage  at  $195, 
a  harness  at  $38.75,  and  a  robe  at  $15.35. 

11.  How  much  does  28,983  exceed  14,299  ? 

12.  Write  3,649,  multiply  it  by  12,  divide  the  product 
by  11,  add  482  to  the  quotient,  and  from  the  sum  subtract 
2872.     What  is  the  remainder  ?     (Indicate.) 

13.  A  grocer  bought  50  bushels  of  potatoes  for  48  cents 
a  bushel,  and  sold  them  for  64^  a  bushel.     What  was  his 
profit  ? 

14.  If  28  Ib.  of  butter  cost  $8.40,  what  will  350  Ib.  cost  ? 

15.  The  divisor  is  75,  the  quotient  184.     What  is  the 
dividend  ? 


152  ARITHMETIC. 

Add  up,  and  from  right  to  left  : 

1.  369  +  2869  +  2864  +  369  =  ? 

9842  +  3984  +  983  +   25  =? 

6894  +  2693  +  4292  +   15  =  ? 

726  +  526  +  39847  +  324  =  ? 

32  +  2864  +  122  +  1592  =  ? 

16  +  294  +  9821  +  296  =? 

954  +   36  +  296  +  324  =  ? 

2989  +  2962  +  3281  +  1692  =  ? 

287  +  392  +  293  +  264  =  ? 

21  3050   9834  =  ? 


Find  the  cost  of  the  following  : 

2.    5    Ib.  sugar          @    7/. 
7    Ib.  beef  @  14/. 

3  bus.  oats         (3  37/. 
9    Ib.  coffee         @  35/. 
4£  doz.  eggs         @  24/. 
6    gal.  kerosene  @    8^. 

|  doz.  oranges    @  48/. 

4  qt.  berries       @  25/. 

3.  What  will  3  bu.  and  2  pecks  of  corn  cost,  at  45/  a 
bushel  ? 

4.  What  is  the  cost  of  8  Ib.  4  oz.  of  honey  at  16/  a 
pound  ?     Of  7}  Ib.  ? 

5.  What  will  4  bu.  apples  cost,  at  18/  a  peck  ? 

6.  What  will  a  pound  of  candy  cost,  at  5/  an  ounce  ? 

7.  What  is  the  cost  of  2  bu.  of  berries,  at  7/  a  quart  ? 

8.  How  many  bushels  of  potatoes,  at  45/  a  bushel,  will 
pay  for  28  sheep,  at  $2.94  each  ? 

9.  At  8/  a  yard,  how  many  yards  of   ribbon  can  be 
bought  for  $4.00  ? 


MISCELLANEOUS.  153 

1.  What  is    a  fraction  ?     An   integer  ?     A   fractional 
unit  ?     An  improper  fraction  ?     A  mixed  number  ? 

2.  Find  the  sum  of  f,  f ,  f ,  and  £. 

5.  What  is  the  common  denominator  of  two  or  more 
fractions  ? 

6.  What  is  the  least  common  denominator  of   two  or 
more  fractions  ? 

Reduce  to  lowest  terms  : 
7-    If,  iff,  «»»,  Hi,  Hi*,  itt- 
Change  the  following  to  48ths : 

Reduce  to  integers  or  mixed  numbers : 

Reduce  to  improper  fractions  : 

10.  16§,  5$,  268$,  16,  54^,  78J§. 
Add: 

11.  28J  12.    6£          13.    14J  14.    16{ 


Ji  _8i_ 

Find  the  difference : 
15.       16*     16. 


Give  results : 

20.  |  of  56.     (Problem.)        22.    }  X  5£  X  A  X  }}  X 

21.  f  of  144.  23.    J  of  }  of  f  of  T^  of  T 


154  ARITHMETIC. 

1.  The  sum  of  two  fractions  is  }| ;  one  of  them  is  ^. 
What  is  the  other  ? 

2.  Multiply  jj  by  f .     Which  is  greater,  the  product  or 
the  multiplicand,  and  how  much  ? 

3.  The  quotient  is   f,  the  dividend  $.     What  is  the 
divisor  ? 

4.  How  do  you  find  divisor  when  quotient  and  dividend 
are  known  ?     How  do  you  find  multiplicand  when  product 
and  multiplier  are  known  ? 

5.  When  the  sum  of  two  numbers  and  one  of  them  are 
known,  how  do  you  find  the  other  ? 

6.  Give  an  example  similar  to  Example  1.     Example  2. 
Example  3.     Find  the  result. 

7-  ?-ft  =  §  11.  f  +  i  +  ?  =  4i 

8.  $  -r-  ?  =  2  12.  ?  +  ll£  =  18J 

9-  §  X  ?  =  A  13.  ?  -  /9  =  ^     . 

10.  I  -  ?  =  fr  14.  ?  X  ?  =  i 

15.  A  coal  dealer  sold  3f  tons  of  coal  to  one  man,  and  7$ 
tons  to  another.     How  much  did  he  sell  to  both  ? 

16.  If  a  load  of  hay  was  bough:  for  $ll£  and  sold  for 
$16|,  what  was  the  profit  ? 

17.  A  teamster  feeds  his  horses  J  a  bushel  of  oats  in  the 
morning,  £  bu.  at  noon,  and  f  bu.  at  night.     How  much 
does  he  feed  daily  ? 

18.  John  gave  $f  for  skates,  $£  for  straps,  and  $|  for  a 
sled.     How  much  did  all  cost  ? 

19.  A  merchant  sold  f  of   a   bushel    of    seeds   to  one 
farmer,  5j  to  another,  and  8   bushels  to  another.     How 
many  bushels  were  sold  in  all  ? 

20.  Write  a  problem  in  addition  of  fractions,  using  a 
mixed  number,  a  fraction,  and  an  integer.     Solve  it. 


MISC  ELL  ANEOUS.  155 

1.  Multiply  together  3580  and  15,  and  divide  the  prod- 
uct by  24  times  75.     (Cancel.) 

2.  How   many    loads    of    apples,    each    containing   22 
bushels,  at  50/  a  bushel,  will  pay  for  132  Ib.  of  butter,  at 
25/  a  pound.     (Cancel.) 

3.  Divide  two  hundred  sixty-seven  million,  one  hundred 
five,  by  twenty-three  thousand,  seventeen. 

4.  Which  is  worth  the  more,  24  J  tons  of  hay  at  $14  a 
ton,  or  68  tons  of  coal  at  $4f  a  ton  ? 

5.  The  product  of  three  numbers  is  360 ;  two  of  them 
are  12  and  6.     What  is  the  other  ?     (Indicate  and  cancel.) 

6.  14  x  18  X  ?  =  12600.    (Factor,  indicate,  and  cancel.) 

7.  When  the  product  of  three  numbers  is  known,  and 
the  product  of  two  of  them,  how  do  you  find  the  third  ? 

8.  Keduce  15^  miles  to  feet. 

9.  How  many  feet  in  a  mile  ?     How  many  rods  ? 

10.  Eeduce  5694  oz.  to  higher  denominations. 

11.  How  many  pounds  in  3£  tons  of  coal  ?  , 

12.  Find  the  cost  of  5  Ib.  8  oz.  of  coffee  at  35/  a  pound. 

13.  Eleven  ounces  is  what  part  of  a  pound  ?    (Question.) 

14.  Find  the  cost  of  6  Ib.  11  oz.  of  candy  at  38/  a  pound. 

15.  At  $.05  an  ounce,  what  is  the  cost  of  3j  pounds,  of 
cloves  ? 

16.  Eeduce  3694  pints  to  higher  denominations. 

17.  How  many  pints  will  a  5-gallon  cask  hold  ? 

18.  3  pints  is  what  part  of  a  gallon  ? 

19.  A  farmer  sold  to  a  merchant  2  firkins  of  butter  of 
56  Ib.  each,  at  24^/  a  pound,  and  bought  4  boxes  of  tea 
weighing  35  Ib.  each,  at  40/  a  pound.     Did  the  merchant 
owe  the  farmer,  or  did  the  farmer  owe  the  merchant,  and 
how  much  ? 


156  ARITHMETIC. 

Oral  Work. 

PARTS   OF  A   DOLLAR. 

Find  the  cost  of  : 

1.  8  boxes  of  berries  at  12£/  a  box. 

2.  24  Ib.  of  coffee  at  25/  a  pound. 

3.  36  doz.  eggs  at  16§/  a  dozen. 

4.  32  pounds  of  sugar  at  6J/  a  pound. 

5.  36  bars  of  soap  at  8J/  a  bar. 

Make  a  bill  of  example  1-5,  and  supply  names  and  date. 

6.  How  much  is  f  of  $1.00  ?    f  of  $1.00  ?    §  of  $1.00  ? 
J  of  $1.00  ?     |  of  $1.00  ?     J  of  $1.00  ? 

Find  the  cost  of : 

7.  60  Ib.  of  coffee  at  33J/  a  pound. 

8.  8  yards  linen  at  37  J/  a  yard. 

9.  40  bushels  of  corn  at  62£/  a  bushel. 

10.  15  yards  of  flannel  at  66|/  a  yard. 

11.  8  bushels  of  wheat  at  75/  a  bushel. 

12.  8  hats  at  87J/  each. 

QUESTIONS   OF   RELATION. 

13.  A  foot  is  what  part  of  J  yard  ? 

14.  A  boy  gave  his  brother  8  marbles,  which  was  f  of 
all  'he  had.     How  many  had  he  ? 

15.  In  a  school  there  are  20  boys,     f  of  the  pupils  are 
girls.      How  many  pupils  in  the  school  ? 

16.  A  pint  is  what  part  of  a  gallon  ? 

17.  A  lineal  foot  is  what  part  of  a  lineal  yard  ? 

18.  A  square  foot  is  what  part  of  a  square  yard  ? 

19.  f  of  my  sheep  are  in  one  pasture,  and  the  remainder, 
12  in  number,  are  in  another.    How  many  in  both  pastures  ? 

20.  What  part  of  f  is  f  ? 


MISCELLANEOUS.  157 

1.  How  many  steps  of  25  inches  each  must  a  person 
take  in  walking  15  miles  ? 

2.  Paid  $565.85  for  6500  pounds  of  honey,  and  sold  it 
at  12^  cents  a  pound.     What  was  the  whole  gain  ? 

3.  Paid  $189  for  flour  at  $6|  a  barrel.     How  many 
barrels  did  I  buy  ? 

4.  The  area  of  Illinois  is  55,405  square  miles,  and  of 
"New  York  49,170  square  miles.     How  much  larger  than 
New  York  is  Illinois  ? 

5.  The  difference  between  two  numbers  is  4,031,  the 
greater  number  is  8,456.     What  is  the  smaller  ? 

6.  The   multiplicand  is  6,412  and  the  multiplier  29. 
What  is  the  product  ? 

7.  The  divistfr  is  48,  the  quotient  514,  and  the  remain- 
der 13.     What  is  the  dividend  ? 

8.  What  is  the  cost  of  8700  Ib.  of  hay  at  $11  a  ton  ? 

9.  The  product  of  three  numbers  is  42,512.     One  of  the 
numbers    is    164,    and    another    15.     What    is   the   third 
number  ? 

10.  If  216  cabinets  cost  $211,320,  what  will  340  cost  ? 

11.  When  hay  is  $25  a  ton,  how  many  barrels  of  flour, 
at   $9   a   barrel,  will   exactly  pay  for  45  tons  of   hay? 
(Indicate.) 

12.  Reduce  f  }££  to  lowest  terms. 

13.  Find  the  sum  of  £ f ,  f ,  and  4^. 

14.  If  9J  yards  cut  from  a  roll  of  cloth  leaves  34f  yards, 
what  is  the  length  of  the  roll  ? 

15.  What  is  the  value  of  3|  times  £  of  |f  ? 

16.  Find  the  number  that  must  be  added  to  f  of  ^  to 
make  |  of  ^. 

17.  What  fraction  must  f  be  divided  by  to  give  3jr  ? 


158  ARITHMETIC. 

1.  Change  ^  to  a  fraction  having  84  for  its  denominator. 

2.  How  many  times  is  ^  +  i  +  i  contained  £  +  £  +  £  ? 

3.  What  fraction  of  5  bushels  is  ^  of  3£  bushels  ? 

4.  Reduce  f  of  ^\  of  ^  of  8 j  to  a  simple  fraction. 

5.  Sold  a  horse  for  $105f,  which  was   J  of  its  cost. 
What  was  its  cost  ?     (Question.) 

6.  What  cost  22£  tons  of  coal  at  $3  J  a  ton  ? 

7.  Bought  3J  bu.  of  corn  for  $4|,  what  was  the  price  ? 

8.  When  $1.25  is  paid  for  £  of  a  cord  of  wood,  what  is 
the  cost  of  one  cord  ?     Of  12f  cords  ? 

9.  If  30  men  can  build  a  wall  in  20  days,  in  how  many 
days  can  $  as  many  men  build  it  ? 

10.  If  |  of  a  store  is  worth  $6000,  what  is  the  whole 
store  worth  ? 

11.  Find  the  sum  of  $13.50,  $2.63,  $5000,  $.32,  $6.13. 

12.  What  is  the  cost  of   60  Ib.  of  crackers  at  $.14  a 
pound,  and  142  loaves  of  bread  at  $.08  a  loaf  ? 

13.  What  will  2134  pair  of  boots  cost  at  $1.75  a  pair  ? 

14.  What  will  212  bu.  of  oats  cost  at  $1.37£  a  bushel  ? 

15.  What  will  75  yd.  of  cloth  cost  at  66f  /  a  yard  ? 

16.  At  $5.12£  a  dozen,  how  many  dozen  knives  can  be 
bought  for  $30.75  ? 

17.  At  $.87£  each,  what  must  be  paid  for  24  books  ? 

18.  How  many  rods  of  fence  are  required  to  enclose  a 
lot  25  rd.  wide  and  twice  as  long  ?     (Diagram.) 

19.  At  $2  a  foot,  what  will  it  cost  to  build  a  stone  wall 
24  rods  long  ? 

20.  What  is  the  distance  in  inches  around  a  room  22 
yards  square  ? 

21.  What  cost  27  in.  of  ribbon  at  60  cents  a  yard  ? 

22.  Define  a  rectangle.     A  square.     Area. 


MISCELLANEOUS.  159 

1.  What  part  of  an  acre  is  130  sq.  rd.  ?     75  sq.  rd.  ? 

2.  Bought  nuts  for  $2  a  bushel  and  sold  them  for  10 
cents  a  quart.     What  did  I  gain  on  5  bushels  ? 

3.  I  burn  a  pint  of  kerosene  every  night.     What  will  a 

4  weeks7  supply  cost  me  at  18  cents  a  gallon  ? 

4.  If  200  Ib.  of  flour  can  be  packed  into  a  barrel,  how 
many  barrels  will  be  needed  to  pack  4  T.  10  cwt.  ? 

5.  What  cost  3  Ib.  8  oz.  of  butter  at  32/  a  pound  ? 

6.  What  is  the  difference  between  25  long  tons,  and 
28  common  tons  ? 

7.  Explain  the  difference  in  the  use  of  a  long  ton  and  a 
common  ton. 

8.  A  coal  dealer  bought  10  car  loads  of  coal,  each  car 
containing  14  long  tons.     How  many  short  tons  did  he 
buy  ?     (Indicate  and  cancel.) 

9.  How  many  hours  in  f  of  a  week  ? 

10.  How  many  dozen  pint  bottles  will  be  needed  to  hold 

5  gal.  3  qt.  of  milk  ? 

11.  A  grocer  buys  a  barrel  of  oil  containing  40  gal.  for 
$40,  and  sells  it  at  $.30  a  pint.     What  does  he  gain  ? 

12.  Reduce  12  A.  144  sq.  rd.  to  square  feet. 

13.  Reduce  60  gal.  3  qt.  1  pt.  to  pints. 

14.  Eeduce  48  miles  to  feet. 

15.  Change  -$y  of  a  mile  to  feet.  ' 

16.  What  part  of  2  bu.  is  1  bu.  5  qt.  ?     (Question.) 

17.  A  rectangular  lot  containing  2648  sq.  ft.  has  a  front- 
age of  262  feet.     What  is  the  other  dimension  ? 

18.  If  the  top  of  your  desk  is  2j  ft.  long  and  18  in.  wide, 
how  many  yards  in  the  four  sides  ? 

19.  It  is  l£  miles  to  the  post-office.     How  many  miles 
must  I  travel  to  go  the  post-office  and  back  four  times  ? 


160  ARITHMETIC. 

1.  What  costs  a  mile  of  wire  at  3  cents  a  foot  ? 

2.  At  5  cents  a  quart,  what  will  be  my  milk  bill  for 
May  and  June  if  I  take  3  quarts  daily  ? 

3.  2  of  48  is  ^T  of  what  number  ?     (Question.) 

4.  A  farm  is  -J  mile  square.     How  many  acres  does  it 
contain  ? 

5.  How  long  must  a  field  be,  that  is  40  rd.  wide,  to 
contain  5  acres? 

6.  What  will  8  Ib.  15  oz.  of  sugar  cost  at  If  a  pound  ? 

7.  In  a  school,  T7y  of  the  pupils  are  girls  ;  there  are  90 
boys.     How  many  pupils  in  the  school  ? 

8.  What  cost  18  dozen  blank-books  at  33  J/  each  ? 

9.  How  many  3-inch  squares  in  a  square  foot  ? 

10.  How  many  yards  of  carpet  J  yd.  wide  will  be  re- 
quired for  a  room  18  ft.  square  ? 

11.  The  area  of  a  sidewalk  a  mile  long,  is  just  one  acre ; 
how  wide  is  it  ?     (Indicate  and  cancel.) 

12.  If  an  iron  rail  is  33  ft.  long,  how  many  rails  will  be 
required  to  lay  a  double-track  railroad  10  miles  long? 

13.  I  have  $570  in  my  safe,  which  is  f  of  what  I  have 
in  the  bank.     How  much  money  have  I  ? 

14.  How  many  square  yards  in  a  room  28  ft.  long  and 
fifteen  feet  wide  ? 

15.  How  many  square  yards  in  a  piece  of  calico  48  inches 
wide  and  48  yards  long  ? 

16.  I  have  a  piece  of  land  200  ft.  deep,  and  fronting 
250  ft.  on  the  street.     I  cut  it  into  50-foot  lots,  and  fence 
each  lot.     What  will  my  fencing  cost,  at  $5  a  rod  ? 

17.  How  many  times  will  a  wheel  5  ft.  in  circumference 
turn  in  going  26  miles  ? 

18.  How  many  square  feet  in  a  room  4  yd.  wide  and  20  ft. 
long? 


MISCELLANEOUS.  161 

1.  How  many  acres  in  a  street  50  feet  wide  and  f  of  a 
mile  long  ? 

2.  How  many  square  yards  of  silk  in  400  feet  of  4-in. 
ribbon  ? 

3.  From  an  acre  of  land  I  sold  10  square  rods  and  also 
a  piece  10  rods  square.     How  much  have  I  left  ? 

4.  A  field  containing  6  acres  is  600  ft.  long.     What  is 
the  distance  around  it  ? 

5.  From   the   product   of   3*    and   4J  take  half   their 
difference. 

6.  If  7  barrels  of  flour  cost  $47,  what  will  21  barrels 
cost  ?     (Indicate  and  cancel.) 

7.  Write  1567849  in  words  ;  in  Roman  Notation. 

8.  What  is  the  difference   between  32  x  534  and  63 
X  542? 

9.  How  many  more  times  is  18  contained  in  216  than  it 
is  in  72  ? 

10.  Multiply  462  by  12,  and  write  the  product  in  figures 
and  words. 

11.  What  number  must  be  added  to  365  to  make  840  ? 

12.  What  number  taken  from  8,473  will  leave  2,416  ? 

13.  7,532  less  what  number  will  give  457  ? 

14.  How  many  hours  are  there  in  January  ? 

15.  The  product  of  two  factors  is  216,  one  of  the  factors 
is  12  ;  what  is  the  other  ? 

16.  Two  men,  who  are  1550  miles  apart,  travel  towards 
each  other,  one  36  miles  a  day,  the  other  40  miles  a  day. 
In  how  many  days  will  they  meet  ? 

17.  Divide  246,752  by  41,  and  prove  your  work. 

18.  What    is    the    difference    between   a   figure    and    a 
number  ? 


162  ARITHMETIC. 

1.  If  9578  is  the  remainder  and  709  the  subtrahend, 
what  is  the  minuend  ? 

2.  Divisor  is  46,  quotient  is  52,  remainder  is  7.     Find 
dividend. 

3.  How  many  pounds  of  sugar  at  9  cents  a  pound,  can 
you  get  for  18  dozen  eggs  at  25  cents  a  dozen  ? 

4.  Multiply  752  by  18 ;  add  234  to  the  product ;  subtract 
562  from  the  sum ;  and  divide  the  remainder  by  24. 

5.  Divide  the  product  of  the  sum  and  difference  of  222 
and  66  by  72.     (Indicate.) 

6.  Write  in  figures,  MDXLI ;  XCXCIX. 

7.  Bought  18  Ib.  of  steak  at  24/,  4J  doz.  eggs  at  36/, 
3  qt.  of  molasses  at  18/,  and  a  bushel  of  potatoes  for 
Make  out  in  the  form  of  a  bill,  and  receipt  it. 

8.  How  many  5-cent  pieces  in  $840  ? 

9.  6020  X  40  X  12  =  18  X  ? 

10.  Eeduce  to  lowest  terms  :  ffc 

11.  Change  to  an  improper  fraction 

12.  Multiply  175f  by  12 ;  124  by  6| ;  6|  by  12|. 

13.  Eeduce  to  whole  or  mixed  numbers  :  ^ff  A ;  ^ly11. 

14.  Divide  the  product  of  4J  and  6|  by  5£. 

15.  Add :   12|,  16|,  24f ,  40J. 

16.  What  is  the  difference  between  84 J  and  42|  ? 

17.  If  a  man  travels  230  miles  in  5j  days,  how  far  can 
he  travel  in  3J  days  ?     (Indicate  and  cancel.) 

18.  If  f  of  a  farm  is  worth  $7000,  what  is  the  whole 
farm  worth  ? 

19.  Multiply  f  of  12|  by  36J.     (Cancel.) 

20.  Divide  27|  by  f  of  8J. 

12.    A  boy  paid  $4§  for  shoes  and  f  9f  for  a  coat.     How 
much  more  did  the  coat  cost  than  the  shoes  ? 


MISCELLANEOUS.  163 

1.  A  stone  wall  5  ft.  high  encloses  a  field  175  feet  long 
and  53  ft.  wide.     How  long  is  the  fence  ? 

2.  A  farmer  kept  his  sheep  in  two  pastures  ;  one-half 
of  his  flock  was  in  one,  and  53  in  the  other.     How  many 
had  he  ? 

3.  A  fourth  of   a  hogshead  of   oil  leaks   out.      How 
many  pint  bottles  can  be  filled  from  the  remainder  ? 

4.  Give  four  factors  of  48. 

5.  What  is  the  difference  between  5  square  feet  and 
5  feet  square  ?     (Illustrate.) 

6.  How  many  square  yards  in  the  surface  of  a  desk  26 
feet  long  and  18  inches  wide  ? 

7.  Reduce  2013  gills  to  higher  denominations. 

8.  How  many  bricks,  8  in.  by  4  in.  by  2  in.,  laid  on  the 
side,  will  be  required  to  pave  a  walk  60  ft.  long  and  5  ft. 
wide  ?     (Indicate  and  cancel.) 

9.  Make    a   receipted    bill    of    the   following,    sold   to 
yourself:   5J  yd.  of   cloth  at  $1.75;  2  pair  of   shoes  at 


10.  How  many  square  feet  of  sidewalk  8  ft.  wide  will 
be  needed  to  make  a  walk  in  front  of  a  lot  8  rd.  wide  ? 

11.  How  many  lots  of  20  sq.  rd.  each  will  15J  acres  of 
land  make  ? 

12.  How  many  feet  in  a  mile  ?  in  f  of  a  mile  ?  in  17| 
miles  ? 

13.  Find  the  product  :  §  X  |  X  f  X  j§-  X  3£  X  4. 

14.  Change  f  to  a  fraction  having  153  for  a  denominator. 

15.  The  sum  of  two  numbers  is  47  f  ,  and  one  of  them  is 
18$.  What  is  the  other  ? 

16.  Divide  14|  by  f  of  19. 

17.  What  part  of  two  yards  is  two  feet  ? 


164 


ARITHMETIC. 


Addition. 

The  following  table  shows  the  number  of  the  boys  and 
girls  registered,  and  the  average  attendance  in  the  schools 
of  Syracuse  for  the  year  1893. 

Add  and  make  the  sums  of  the  totals  alike. 


NUMBER  REGISTERED. 

AVERAGE  DAILY 
ATTENDANCE. 

SCHOOLS. 

m 

1 

d 

00 

3 

•3 

& 

O 

I 

1 

O 

"o 
ri 

High    .... 

373 

558 

290 

435 

Salina  .... 

273 

261 

215 

207 

Jefferson  .     .     . 

168 

140 

. 

142 

118 

Genesee    .     .     . 

263 

197 

,     t 

210 

158 

Prescott    .     .     . 

358 

329 

287 

257 

f 

Seymour  . 

420 

502 

325 

388 

. 

Putnam    .     .     . 

402 

457 

. 

332 

364 

. 

Irving  .... 

225 

198 

. 

172 

158 

. 

Delaware  .     .     . 

287 

307 

221 

228 

. 

Porter.     .     .     . 

485 

515 

365 

375 

Gere     .... 

196 

198 

158 

160 

. 

Danforth  .     .     . 

195 

207 

163 

159 

Brighton  .     .     . 

241 

292 

182 

213 

. 

Rose     .... 

9 

9 

. 

8 

7 

. 

Clinton     .     .     . 

289 

270 

. 

228 

218 

Vine     .... 

109 

122 

. 

82 

89 

Grace  .... 

209 

179 

. 

173 

145 

Merrick    .     .     . 

177 

184 

152 

153 

Madison   .     .     . 

389 

409 

315 

311 

Bassett     .     .     . 

92 

81 

78 

72 

Frazer  .... 

223 

243 

183 

207 

Townsend      .     . 

190 

199 

170 

173 

. 

Franklin  .     .     . 

570 

514 

. 

469 

445 

May      .... 

289 

302 

219 

254 

Montgomery 

324 

260 

286 

225 

. 

Adams      .     .     . 

163 

168 

144 

149 

Total  .     .     . 

•     • 

•     • 

Total, 

PARTS   OF   A  DOLLAR.  165 

Oral  Work. 

PARTS   OF  A   DOLLAR. 

1.  At  6  J  cents  apiece,  how  many  pencils  can  be  bought  for 
i  of  a  dollar  ?  for  $  J  ?  for  $4  ? 

2.  At  8j/  a  box,  how  many  boxes  of  berries  can  be 
bought  for  $1  ?  for  $  \  ?  for  75  cents  ?  for  $2  ? 

3.  At  12^  cents  each,  how  many  tablets  can  be  bought 
for  $3  ?  for  $  \  ? 

4.  At  16f/  a  dozen,  how  many  dozen  eggs  can  be  bought 
for  $5  ?  for  $£•? 

5.  How  many  pounds  of  coffee  at  25/  a  pound,  can  be 
bought  for  $3.00  ?  for  $£  ? 

6.  How  many  straw  hats  can  be  bought  for  $2.00  at  33J 
cents  each  ? 

7.  At  37J/  a  pound,  how  many  pounds  of  coffee  can  be 
bought  for  $3.00  ?  for  $J  ? 

8.  How  many  days  must  James  work,  at  50/  a  day,  to 
earn  $5.00  ? 


QUESTIONS   OF   RELATION. 

1.  A  man  deposited  in  the  bank  f  of  his  money  which 
was  $3000.     How  much  had  he  ? 

2.  What  part  of  a  yard  is  one-half  a  foot  ? 

3.  What  part  of   the  week  is  passed  at   midnight   on 
Wednesday  ? 

4.  John  had  $12.     He  spent  $4  for  a  coat.     What  part 
of  his  money  remains  ? 

5.  A  gentleman  divided  50  cents  among  5  children.     To 
four  of  them  he  gave  f  of  the  money.     How  much  did  the 
fifth  receive  ? 

6.  At  midnight  on  the  16th  of  June,  what  part  of  the 
month  has  passed  ? 


166  ARITHMETIC. 

1.  If  J  of  §  of  a  piece  of  land  is  worth  $5000,  what  is 
the  whole  piece  worth  ? 

2.  Change  ^,  ^,  ^  to  lowest  terms. 

3.  If  a  man  can  travel  15f  miles  in  one  day,  how  far 
can  he  travel  in  5  J  days  ? 

4.  A  man  received  $91 J  for  working  30 J  days.     How 
much  did  he  earn  a  day  ? 

5.  What  number  is  that  from  which,  if  2Sf  is  taken, 
the  remainder  will  be  40  J  ? 

6.  Find  the  cost  of  f.  of  130  acres  of  land  at  ^  of  $81 
an  acre.     (Indicate  and  cancel.) 

7.  What  number  multiplied  by  $  will  give  4f  ? 

8.  In  5g  acres,  how  many  building  lots  of  $  of  an  acre 
each? 

9.  What  part  of  10  miles  is  §  of  12  miles  ? 

10.  f  of   a  farm  is  worth  $8000.     What  is  the  whole 
farm  worth  ? 

11.  If  3  be  added  to  both  terms  of  the  fraction  f ,  will 
its  value  be  increased  or  diminished,  and  how  much  ? 

12.  A  girl  sold  a  pair  of  skates  for  $1^,  which  was  f  of 
their  cost.     How  much  did  she  lose  ? 

13.  Multiply  25-|  by  f . 

14.  How  many  acres  in  £  of  a  mile  of  street  66  ft.  wide  ? 

15.  If  3}  yd.  of  gingham  cost  22  cents,  how  many  yards 
can  be  bought  for  75  cents  ? 

16.  What  part  of  a  ton  is  175  Ib.  ?     (Question.) 

17.  How  many  sheep,  at  $8  each,  can  be  exchanged  for 
12  horses  at  $250  each  ?     (Indicate  and  cancel.) 

18.  Divide  §  by  |. 

19.  If  |  of  my  salary  is  $1200,  what  is  my  salary  ? 


MISCELLANEOUS.  167 

1.  Fifteen  men  do  a  piece  of  work  in  8  days.     How 
long  will  it  take  8  men  to  do  it  ? 

2.  Divisor  is  3f,  quotient  is  4f .     Find  the  dividend. 

3.  If  If  yd.  of  silk  cost  $llj,  what  will  one  yard  cost  ? 

4.  If  a  roll  of  carpet  containing  80  yards  is  worth  $160, 
what  is  f  of  a  yard  worth  ? 

5.  How  many  quarts  of  nuts  at  8^  cents  a  quart,  will  it 
take  to  buy  5  J  bu.  of  apples  at  $}  a  bushel  ? 

6.  From  a  hhd.  of  molasses  containing  56  gal.  2  qt., 
there  were  sold  25  gal.  1  pt.     How  many  quarts  remained  ? 

7.  Change  29  gal.  2  qt.  1  pt.  to  gills. 

8.  How  many  rods  of  fence  will  be  required  to  enclose 
a  rectangular  field  95  yd.  long  and  60  yd.  wide  ? 

9.  A  farmer  divides  his  farm  of  425  acres  into  fields  of 
12£  acres  each.     How  many  fields  has  he  ? 

10.  If  2f  yd.  of  ribbon  cost  45  cts.,  what  will  3£  yd. 
cost? 

11.  How  many  yards  in  5  pieces  of  cloth,  each  contain- 
ing 19£  yards  ? 

12.  The  product  is  960,  the  multiplier  is  52.     Find  the 
multiplicand. 

13.  The  width  of  a  room  is  f  of  its  length.     How  many 
square  feet  in  the  floor,  if  the  width  is  18  ft.  ? 

14.  ,J  of  what  number  equals  200  ? 

15.  How  many  square  yards  in  the  four  walls  and  ceil- 
ing of  a  room  20  ft.  long,  15  ft.  wide,  and  12  ft.  high  ? 

16.  A  lady  had  $36.84.     She  spent  J  of  it  for  a  cloak 
and  ^  for  a  pair  of  shoes.     How  much  was  left,  and  what 
fraction  of  the  entire  sum  was  it  ? 

17.  How  many  yards  of  carpet,  1  yd.  wide,  will  be  needed 
for  a  room  24  ft.  by  18  ft.  ? 


168 


ARITHMETIC. 


Written  Work 
1-     J  X    | 
8.     fX    | 

3.       |X     J 

4-  H  x  A 

6.    «  X  A 

16.  38946f    X  9 

17.  25986JI  X  8 

18.  39825§    X  6 

19.  298f  J  X  4 

20.  39846^  X  25 


6.  32-j    X    4 

7.  14J     X  16 

8.  135  §    X  18 

9.  75J    X  15 
18^x20 


10. 


11.  16  X  4J 

12.  18  X  8-J 

13.  46  X  3f 

14.  129  x  15f 

15.  161  X  25T87 


21.  36982  x    5| 

22.  4986  X  16f 

23.  28761  X  18£ 

24.  39840  X  16H 

25.  26358  X  4| 


Reduce  the   following  compound   fractions   to   simple 
fractions : 

26.  |of  Jof  A  29.   fcofiJofH 

27.  |  of  JJ  of  if  30.    §  of  |  of  | 

28.  fof  JJofff  31.    f  off  of  A 

Divide,  and  prove  by  multiplication : 


1. 

M 

-  A 

6. 

35| 

--5 

11. 

26 

-*-2i 

2. 

§'•*•* 

7. 

26| 

-f-7 

12. 

13 

-If 

3. 

ft-* 

•A 

8. 

ISA 

-r-5 

13. 

16 

-^-2i 

4. 

if  -  T\ 

9. 

15f 

-j-12 

14. 

84 

-5^ 

5. 

t-M 

10. 

121| 

-f-6 

15. 

69 

-7| 

16. 

2834^ 

-J-  6 

20. 

21983 

~=~  i 

17. 

3984§ 

--5 

21. 

39562 

-T-    ^ 

r 

18. 

2693f 

-8 

22. 

17523 

-r-  I 

! 

19. 

2345f 

-^  6 

23. 

28884 

-5-  1 

b 

24. 

iof 

1  -*- 

f   Of   f 

27. 

T       X 

1  X  T6T  -5-  f 

X6 
•yY 

25. 

f  of 

i- 

|of  A 

28. 

1   x 

ixi 

i  ^~ 

A 

x  H 

26. 

}  of 

li-H 

|of| 

29. 

HX, 

li-*-    1 

IX 

A 

X  2 

REVIEW.  169 

1.  Find  the  cost  of  15  doz.  collars  at  $.16|  each. 

2.  Paid  $24  for  cuffs  at  16  f/  a  pair.     How  many  dozen 
pairs  were  bought  ? 

3.  If  one  bushel  of  wheat  is  worth  $1.37^,  how  many 
bushels  can  be  bought  for  $198  ? 

4.  Divide  $3,542,305  by  864. 

5.  Divide  §  of  24  qt.  of  nuts  among  20  boys. 

6.  If  4  qt.  of  nuts  cost  25  cents,  what  will  half  a  bushel 
cost?     (Indicate  and  cancel.) 

7.  If  I  of  a  load  of  hay  is  worth  $7,  what  will  2  loads 
be  worth  ?     (Indicate  and  cancel.) 

8.  2J  X  3£  =  ?         2J  -r-  3£  =  ? 

9.  At  80/  a  lb.,  what  will  5  oz.  of  tea  cost  ? 

10.  How  many  sq.  yards  in  the  surface  of  a  table  12  ft. 
by  5  ft.  ? 

11.  £  of  16  is  £  of  what  number  ? 

12.  108  is  J  of  $  of  what  number  ? 

13.  If  one  man  can  do  a  piece  of  work  in  12§  days,  how 
long  will  it  take  5  men  to  do  it  ? 

14.  A  field  is  825  ft.  long  and  396  ft.  wide.     How  many 
rods  of  fence  will  be  required  to  enclose  it  ? 

15.  How  many  bushels  of  oats  at  $f  a  bushel,  will  pay 
for  g  of  a  barrel  of  flour  at  $4.75  a  barrel  ? 

16.  How  many  arithmetics  at  37J/  each  can  be  pur- 
chased for  $384  ? 

17.  How  many  pounds  of  butter  at  25/  a  pound  can  be 
bought  for  $8.50  ?  at  37/  ? 

18.  How  many  dozen  eggs  at  12 \p  a  dozen  can  be  bought 
for  $3  ?  for  $11  ?  for  $3.75  ? 

19.  At  $.62^  a  yard,  how  many  yards  of  cloth  can  be 
bought  for  $31.50  ? 


170  ARITHMETIC. 

1.  What  are  unlike  fractions  ?     How  are  they  added  ? 

2.  Write  three  unlike  fractions  and  add  them. 

3.  Write  two  unlike  fractions  and  find  their  difference. 

4.  Write  a  compound  fraction  having  four  simple  frac- 
tions and  change  it  to  a  simple  fraction. 

5.  Write  a  complex  fraction  with  an  integer  for  the 
numerator  and  a  fraction  for  the  denominator,  and  reduce 
it  to  its  simplest  form. 

6.  Write  three  other  forms  of  complex  fractions  and 
change  them  to  simple  fractions. 

7.  Can  you  write  still  other  forms  of  complex  fractions  ? 

8.  James  had  }  of  an  apple  and  gave  J  of  £  of  it  to  his 
brother.     What  part  did  he  give  to  his  brother  ?     What 
part  remained  ? 


9      --,  »? 

'  2*  f  •  13J-          4 

10.  How  many  days  in  £  of  a  common  year  ? 

11.  How  much  cloth  will  be  required  for  3  doz.  vests 
allowing  f  yd.  for  each  ? 

12.  What  will  one  orange  cost  if  3  oranges  cost  5/  ? 

13.  How  many  days  must  a  boy  work  to  earn  $5^  if  he 
earns  $|  a  day  ? 

14.  168  is  f  of  what  number  ? 

15.  §  of  12  are  how  many  times  3  ? 

16.  §  of  12  is  £  of  what  number  ? 

17.  I  bought  3  tons  of  coal,  and  used  f  of  a  ton  one 
month  and  T9^  of  a  ton  the  next  month.     How  much  was 
left? 

18.  A,  B,  and  C  own  a  melon  ;  A  owns  J,  B  f  ,  and  C 
the  rest.     What  part  does  C  own  ? 

19.  3  pints  is  what  part  of  3  gallons  ?     (Question.) 


REVIEW.       ^gA-  CALiFO  171 

1.  What  is  a  factor  ?  a  prime  number  ?   a  multiple  ? 

2.  What  are  the  prime  factors  of : 

72;  64;  48;  32;  80? 

3.  Write  all  the  prime  numbers  between  10  and  40. 

4.  Write  the  composite  numbers  between  59  and  71, 
and  find  their  prime  factors. 

5.  What  are  the  prime  factors  of  484  ? 

6.  What  is  the  greatest  common  divisor  of  25  and  150  ? 

7.  12  X9X6X  20 --2x3x3x4x5. 

8.  75  X  33  x  2  x  125  --  16  X  150. 

9.  What  number  is  a  multiple  of  5  ? 

10.  Write  four  numbers  that  are  multiples  of  6.     Are 
there  any  more  ?     What  is  the  least  multiple  of  6  ? 

11.  What  is  the  least  common  multiple  of  18,  28,  and  30  ? 

12.  Find  the  sum  of  the  prime  numbers  from  0  to  30. 
From  30  to  60. 

13.  Divide  504  by  82,  using  prime  factors  and  cancel- 
lation.    Prove  the  work. 

14.  Divide  28  X  56  X  15  by  6  X  5  x  14.     (Cancel.) 

15.  At  7/  a  pound,  how  many  pounds  of  sugar  can  be 
bought  for  $60.55  ? 

16.  A  man  bought  700  bushels  of  wheat  at  $.95  a  bushel. 
He  sold  256  bushels  at  $1.10  a  bushel,  45  bushels  at  $1.15 
a  bushel,  and  the  remainder  for  $395.     How  much  was 
his  gain  ? 

17.  At  the  rate  of  6  pencils  for  48  cents,  how  many  pen- 
cils can  be  bought  for  32/  ?     (Indicate.) 

18.  £  pt.  is  what  part  of  f  pt.  ? 

19.  If  gold  is  worth  $18.60  an  oz.,  what  is  the  value  of 
a  cup  that  weighs  6  oz.  5  pwt.  ? 

20.  (5  +  3)  X  4  minus  5  +  3x4  =  ? 


172  ARITHMETIC. 

1.  What  number  other  than  71  will  evenly  divide  8662  ? 

2.  Why  do  you  change  fractions  to  a  common  denom- 
inator before  adding  them  ? 

3.  Keduce  T%,  ?\,  }f  to  205ths. 

4.  Edwin  had  $25j.     He  spent  $J  for  skates,  $1J  for 
gloves,  and  $6 J  for  a  suit  of  clothes.    How  much  was  left  ? 

5.  13J   is   divisor,    1080    is   quotient,    12J   remainder. 
Find  the  dividend. 

6.  If  6  spoons  cost  f  9|,  what  will  15  spoons  cost  ? 

(*  +  %)  X  M       0 
14J  -  2J 

8.  8  is  what  part  of  13  ? 

9.  76  -f-  228  =  ?     4J  -r-  ?  =  10. 

10.  ^T  of  a  hhd.  leaked  out.     How  many  2£  pint  cans 
can  be  filled  from  the  remainder  ? 

11.  ^  of  a  flock  of  sheep  was  sold  and  27  were  left. 
How  many  in  the  flock  at  first  ? 

12.  How  many  square  inches  in  an  8  ft.  square  ? 

13.  Find  the  area  in  square  yards  of  a  lawn  35  by  28  ft. 

14.  How  many  lots  10  rd.  deep  and  5  rd.  wide  can  be 
sold  from  a  5  A.  field  ? 

15.  J.  F.  Worclen  bought  of  Dey  Bros,  the  following: 
18  yd.  lace  at  16|/  a  yard,  4£  dozen  ties  at  $1.50  a  dozen, 
3  dozen  handkerchiefs  at  $.25  each.     Make  out  the  bill, 
and  receipt  it  ? 

16.  4003  X  1000  -f-  201  =  ? 

17.  Bought  25  Ib.  of  butter  at  25    cents  a  pound.     I 
gave  in  part  payment  35  Ib.  of  cheese  at  12  cents  a  pound, 
and   paid   the  remainder   in   cash.     What   did   I   pay   in 
cash  ? 


REVIEW.  173 

1.  How  many  cheeses  of  45  Ib.   each,  at  12^  cents  a 
pound,  will  pay  for  15  bbl.  of  apples,  each  containing  3  bu. 
at  87J  ct.  a  bushel  ?     (Indicate.) 

2.  13|  +  14|i  -  4J  =  ? 

3.  Multiply  seven  thousand  and  five  by  three  hundred 
five. 

4.  Add  210  ;  15,262,986 ;  15,438  ;  then  multiply  \  of  the 
sum  by  130. 

5.  From  125|  yd.  of  cambric  were  sold  87T\  yd.    What 
remained  ? 

6.  8754321  +-  873  =  ?     9853021  +  901  =  ? 

7.  How  many  half-pint  bottles  will  be  needed  to  hold 
2J  gal.  of  catsup  ? 

8.  Reduce  21240  pt.  to  bushels,  etc. 

9.  A  train  moves  at  the  rate  of  a  mile  in  2  min.     In 
how  many  hours  will  it  go  330  miles  ? 

10.  A  man  having  420J  miles  to  go  has  traveled  193f 
mi.     How  many  miles  has  he  still  to  go  ? 

11.  How  long  will  20  bu.  of  oats  last  a  horse  if  he  is  fed 
8  qt.  a  day  ? 

12.  Divide  $9340526  equally  among  105  people. 

13.  At  3  ct.  a  gill,  what  will  560  gal.  cost  ? 

14.  16  J  +  lOg-  +  120£  +  96  +  38^  =  ? 

15.  Remainder  56|,  minuend  379£ ;  what  is  the  subtra- 
hend? 

16.  Subtrahend  297^ ;  remainder  194£ ;  find  the  minu- 
end. 

17.  U648  +  9718  +  23149  +  7116  +  73999  +  1476  =  ? 

18.  At  $1.75  a  sq.  rod,  find  the  cost  of  6  acres  of  land. 

19.  (52  +  35)  X  6  plus  52  +  35  X  6  =  ? 

20.  16  +  3  x5  minus  31  =  ? 


174  ARITHMETIC. 

1.  Write  an  improper  fraction,  and  change  it  to  a  mixed 
number. 

2.  Find  the  product  of  f ,  |f ,  f,  f . 

3.  Divide  the  largest  of   the  above  fractions  by  the 
smallest. 

4.  Buy  4  bu.  2  pk.  of  nuts  at  $1.60  a  bu. 

5.  How  many  barrels  of  flour  will  19236  Ib.  make  ? 

6.  A  boy  spent  f  of  his  money,  and  had  $1.50  left; 
how  much  had  he  at  first  ?     (Question.) 

7.  I  bought  8  cwt.  10  Ib.  of  sugar  for  $81,  and  sold  it 
at  12/  a  pound.     What  was  my  gain  ? 

8.  How  many  square  feet  in  a  floor  20  ft.  9  in.  long  and 
17  ft.  6  in.  wide  ? 

9.  If  a  lot  is  198  ft.  long,  and  132  ft.  wide,  how  many 
rods  around  it  ? 

10.  A  lot  contains  3  A.  and  is  20  rd.  wide ;  how  long  is 
it? 

11.  Change  8f  to  25ths. 

12.  Find  the  product  of  7 j-  and  9J. 

13.  The  product  of  two  factors  is  25  J,  one  factor  is  8 £ ; 
what  is  the  other  ? 

14.  I  bought  7  bu.  of  apples  at  $.67£  a  bu.     How  much 
change  should  I  have  left  from  a  two-dollar  bill  ? 

15.  Multiply  2i  by  j-  and  divide  the  product  by  Ij. 

16.  John  had  $3.60  left  after  spending  |  of  his  money. 
How  much  had  he  at  first  ?     (Question.) 

17.  Find  the  area  of  a  floor  18J  ft.  long  and  4  yd.  wide. 

18.  How  much  will  8  bu.  3  pk.  of  potatoes  cost  at  $.20  a 
peck  ? 

19.  9f +  7|.+  6A  =  ? 

20.  Name  two  equal  factors  of  121. 


CHAPTER  IV. 


PLASTERING  AND  PAINTING. 

Plastering  and  painting  are  usually  done  by  the  square 
yard. 

Deductions  are  frequently  made  for  openings. 

Windows  and  doors  are  openings. 

1.    A  room  is  18  ft.  long,  12  ft.  wide,  and  8  ft.  high. 
How  many  square  yards  in  the  walls  and  ceiling  ? 

In  problems  of  this  kind  first  make  a  diagram  represent- 
ing the  four  walls  in  a  line. 

The  ceiling  may  be  represented  as  extend-        ,„!?  FT.__  ^ 
ing  from  a  side  wall  or  an  end  wall. 

Draw   this    diagram    (enlarged)    on    stiff 
paper,  then  cut  and  fold  the  pattern  to  rep-      « 
resent  the  walls  and  ceiling  of  the  room. 


o 

z 


18  FT. 


12  FT. 


18  FT. 


12  FT. 


SOLUTION.  —  The  length  of  the  four  walls  is  2  X  (18  ft. 
+  12  ft.)  =  60  ft. ; 

Area  of  4  walls,  60  ft,  by  10  ft.  =  600  sq.  ft. 

Area  of  ceiling,  18  ft.  by  12  ft.  =  216  sq.  ft. 

Area  of  four  walls  and  ceiling  =  816  sq.  ft.  =  77f  sq.  yd. 

2.  If  in  the  room  mentioned  above  there  are  two  doors, 
3  ft.  by  7  ft.,  and  4  windows  3  ft.  by  6  ft.,  how  many  square 
yards  remain  in  the  four  walls  and  ceiling  ? 

Represent  these  doors  and  windows  on  the  diagram. 

175 


176  ARITHMETIC. 

To  THE  TEACHER.  —  See  that  the  pupil  draws  all  dia- 
grams to  scale  —  that  is,  in  proper  relative  proportions. 

3.  How  much  will  it  cost  at  25  cents  a  square  yard  to 
plaster  the  room  mentioned  in  Example  1,  full  deductions 
being  made  for  openings  ? 

4.  What  will  it  cost  at  33J  cents  a  square  yard  to  plas- 
ter the  walls  and  ceiling  of  a  room  24  ft.  long,  18  ft.  wide, 
and  9  ft.  high  ?     The  room  has  3  doors  3  ft.  by  7  ft.,  and 
6  windows  3  ft.  by  6  ft.     One-half  of  the  openings  deducted. 
(Diagram.) 

5.  How  many  square  yards  of  plastering  in  a  room 
40  ft.  long,  30  ft.  wide,  and  12  ft.  high,  deducting  80  sq.  ft. 
for  openings  ? 

6.  At  35/  a  sq.  yard,  what  will  it  cost  to  plaster  a  room 
18  ft.  square  and  9  ft.  high,  having  3  doors  7  ft.  by  3  ft., 
and  5  windows  6  ft.  by  3  ft.,  no  allowance  for  openings  ? 

7.  A  lot  100  ft.  by  200  ft.  is  enclosed  by  a  tight  board 
fence  5  ft.  high.     At  6j/  a  square  yard,  what  will  it  cost 
to  paint  both  sides  of  it  ? 

8.  What  will  it  cost  to  paint  the  outside  of  a  freight 
car  3  coats,  at  7  cents  a  sq.  yard  for  each  coat,  the  car 
being  25  ft.  long,  9  ft.  high,  and  8  ft.  wide  ? 

9.  Write  an  original  problem  for  plastering  a  room. 
Make  a  diagram  of  it,  and  solve. 

10.  Write  an  original  problem  for  painting.     Make  dia- 
gram, and  solve. 

11.  The  room  in  Example  6  has  a  wainscoting  3  ft.  high. 
How  many  square  yards  of  wainscoting  ? 

12.  Plaster  a  room  having  the   following   dimensions : 
length  40  ft.,  width  28  ft.,  height  16  ft.     Deduct  for  12 
windows,  7  ft.  by  3  ft.,  and  4  doors  9  ft.  by  3  ft.  6  in. 
What  is  the  cost  at  25  cents  a  square  yard  ? 


CARPETING   ROOMS.  177 

13.  Paint  the  outside  of  a  cubical  box,  3  ft.  X  3  ft.  X 
3  ft.  with  3  coats  of  paint.     What  is  the  cost  at  6  cents  a 
square  yard  for  each  coat  ? 

14.  How  many  square  feet  of  boards  necessary  to  con- 
struct a  box  4  ft.  long,  3  ft.  wide,  and  2£  ft.  high,  with 
cover  ? 

15.  How  many  flag-stones  5£  by  5  ft.  will  be  required  for 
a  sidewalk  covering  275  sq.  feet  ? 

16.  At  18/  a  square  yard,  what  will  it  cost  to  plaster 
the  ceiling  and  the  four  walls  of  a  room  that  is  18  ft.  long, 
15  ft.  wide,  and  9  ft.  high  ? 

17.  At  30/  a  square  yard,  what  will  be  the  cost  of  ce- 
menting the  walls   and  floor  of   a   basement  40  ft.  long, 
30  ft.  wide,  and  8  ft,  high? 

18.  A  cistern  is  12  ft.  square  and  9  ft.  deep.     What  will 
it  cost  to  cement  it  at  12 £/  a  sq.  yard  ? 

19.  What  will  be  the  cost  of  turfing  a  lawn  50  ft.  by  38 
ft.  at  9/  a  square  yard  ? 

20.  What  is  a  rectangle  ? 

CARPETING  ROOMS. 

In  carpeting  rooms,  it  frequently  occurs  that  more  car- 
peting must  be  purchased  than  is  needed  to  cover  the  floor. 
This  waste  is  often  necessary  to  make  the  patterns  match. 
A  part  of  one  outside  strip  must  sometimes  be  turned  under. 
All  this  waste  must  be  paid  for  by  the  purchaser. 

If  borders  are  used,  there  is  a  waste  of  %  the  breadth  of 
the  border  in  mitering.  (Illustrate.) 

1.  How  many  sq.  yards  in  the  surface  of  a  floor  18  ft. 
long  and  15  ft.  wide  ?     (Diagram.) 

2.  How  many  lineal  yards  of  carpet  1  yd.  wide  must  be 
purchased  to  cover  it  ? 


178  ARITHMETIC. 

3.  How  many  lineal  yards  of  carpet  £  yd.  wide,  will  be 
needed  to  cover  it  ? 

How  long  and  how  wide  is  each  lineal  yard  ? 

What  part  of  a  square  yard  will  it  cover  ?  Ans.  £  sq.  yd. 

How  many  times  is  J  sq.  yard  contained  in  30  sq.  yd.  ? 

4.  How  many  yards  of  carpet  }  yd.  wide  will  be  required 
for  a  hall  18  ft.  wide  and  30  ft.  long,  the  strips  running 
the  long  way  of  the  hall  ?     How  many  yards  must  be  pur- 
chased if  the  strips  run  the  short  way  ? 

Make  a  diagram  showing  the  strips  or  breadths. 
How  many  lineal  yards  in  each  strip  ? 
How  many  strips  ? 

SOLUTION.  —  Since  one  strip  covers  a  space  £  yd.  wide,  it 
will  take  as  many  strips  to  cover  a  space  6  yd.  wide,  as 
£  yd.  is  contained  times  in  6  yd.  =  8  strips. 

8  strips  each  10  yd.  long  =  80  lineal  yards. 

5.  At  $1.25  a  yard,  what  will  it  cost  to  carpet  a  hall 
11 J  ft.  wide  and  28  ft.  long,  the  carpet  being  1  yard  wide. 

How  many  yards  long  is  each  strip  ? 
How  many  strips  ? 

6.  How  much  would  the  carpet  cost  if  there  were  a  waste 
of  1 J  yd.  for  matching  ? 

NOTE.  —  The  latter  of  the  two  methods  indicated  above 
is  the  more  practical. 

.  7.  How  many  yards  of  ingrain  carpet  1  yd.  wide  will  be 
required  for  a  floor  17  ft.  wide  and  20  ft.  long,  strips  run- 
ning lengthwise  ?  (Diagram.) 

How  many  yards  long  is  each  strip  ? 

How  many  strips  would  be  needed  if  the  room  were  15  ft. 
wide  ?  How  many  if  it  were  18  ft.  wide  ? 

It  being  17  ft.  wide,  how  many  strips  must  be  purchased  ? 

How  much  of  the  last  strip  is  to  be  turned  under  ? 


CARPETING   ROOMS. 


179 


8.  How  many  yards  of  carpet  f  yd.  wide  will  be  re- 
quired to  cover  a  floor  25  ft.  square  ? 

9.  Write  an  original   problem   for  carpeting   a  room. 
Draw  a  diagram,  and  solve  it. 

10.  At  $1.15  a  yard,  what  will  be  the  cost  of  carpeting 
a  room  8  yd.  long  and  5§  yd.  wide,  with  carpeting  J  yd. 
wide,  allowing  If  yd.  for  waste,  and  $3  for  making  and 
laying  ? 

11.  A  sidewalk  10  ft.  wide  is  to  be  laid  on  the  4  sides  of 
a  lot  100  ft.  square. 

At  25/  a  sq.  foot, 
what  will  be  the  cost  ? 
The  walk  will  be 
110  ft.  long  on  each 
of  the  four  sides,  as 
shown  by  the  dia- 
gram. The  entire 
length  of  the  walk  is 
4  X  110  ft.  =  440  ft. ; 
this  multiplied  by  the 
width  of  the  walk  will 
give  its  area. 

12.  What  would  be  the  cost  of  a  5-foot  walk  laid  on  the 
inside  of  the  lot,  close  to  the  sides  ? 

13.  A  man  builds  a  house  45  by  35  ft.,  on  a  lot  60  by 
150  ft.     How  many  sq.  yards  has  he  left  for  a  garden  ? 

14.  What  would  it  cost  to  build  a  tight  fence  5  ft.  high, 
around  the  above  lot,  at  25/  a  square  yard  ? 

15.  What  is  the  cost  of  a  farm  80  rods  square,  at  $50  an 
acre  ? 

16.  How  long  is  a  rectangular  field  that  contains  50  acres 
and  is  80  rods  wide  ? 


i                              110  FT. 

100  FT. 

1                                         8 

•JJOOL 

•JJ  OU 

180  ARITHMETIC. 

PAPERING    WALLS. 

A  roll  of  wall  paper  is  commonly  8  yards  long  and  18 
inches  wide. 

A  double  roll  is  16  yards  long. 
Borders  are  sold  by  the  lineal  yard. 

1.  A  room  is  18  ft.  by  15  ft.,  and  9  ft.  high ;  making  no 
deduction  for  openings,  how  many  square  yards  in  the  four 
walls  and  ceilings  ?     (Diagram.) 

2.  How  many  sq.  yards  will  one  roll  cover  ? 

3.  How  many  rolls  will  be  needed  to  paper  the  room  ? 

4.  If  the  room  has  2  doors  3  ft.  by  8J  ft.,  and  4  win- 
dows 3  ft.  by  6£  ft.,  how  many  sq.  yards  of  surface  are  to 
be  covered  ? 

5.  How  many  rolls  will  cover  it  ? 

6.  At  33 \fl  a  roll,  what  will  be  the  cost  of  papering  ? 

7.  At  50/  a  lineal  yard,  what  will  the  border  cost  ? 

8.  A  hall  is  12  ft.  wide,  38  ft.  long,  and  10  ft.  high. 
The  area  of  the  openings  is  117  sq.  feet.     (Diagram.) 

The  paper  costs  38/  a  roll. 

The  border  costs  66|/  a  yard. 

Cost  of  putting  on:  2  men  1J  days  each  at  $2  a  day. 

Full  deductions  made  for  openings. 

Find  the  entire  cost  and  make  bill. 

9.  What  will  be  the  cost  of  carpeting  the  hall   men- 
tioned above,  with  carpet  f  yd.  wide  at  $1.50  a  yard  ? 

10.  A  sitting-room  is  20  ft.  by  17  ft.,  and  10  ft.  high. 
It  has  3  doors  2  ft.  6  in.  by  7  ft.,  and  4  windows  3i  ft.  by 
6  ft.     How  many  rolls  of  paper  will  cover  the  walls  and 
ceiling,  deducting  \  the  area  of  the  openings  ? 

11.  At  $1.15  a   yard,  what  will  it  cost  to  carpet   the 
above  sitting-room  with  carpet  1  yd.  wide  ? 


BEVIEW.  181 

Review. 

1.  How  many  square  yards  in  a  lot  16  rods  long  and  10 
rods  wide  ? 

2.  How  many  lineal  feet  of  fence  will  enclose  this  lot  ? 

3.  A  farmer  divided    his  farm,  containing  150  acres, 
3  roods  of  land,  among  his  4  sons  and  2  daughters  equally. 
How  much  did  each  receive  ? 

4.  How  many  lots  of  20  sq.  rods  each  will  J  of  a  square 
mile  make  ? 

5.  How  many  rods  of  fence  will  enclose  a  lot  J  of  a 
mile  square? 

6.  How  many  4-in.  squares  may  be  cut  from  a  square 
foot  of  paper  ? 

7.  What  part  of  an  acre  in  a  field  30  rods  by  4  rods  ? 

8.  How  many  square  feet  of  glass  in  6  windows  of  8 
panes  each,  each  pane  being  14  by  12  inches  ? 

9.  What  will  it  cost  to  pave  a  street  2^  miles  long  and 
2£  rods  wide,  at  $12  per  square  rod  ? 

10.  How  many  yards  of  oil-cloth  8  ft.  wide  will  cover  a 
floor  32  by  22  ft.,  if  the  strips  run  lengthwise,  allowing 
1  yard  for  waste  ? 

11.  How  many  yards  of  crash  18  inches  wide  will  cover 
a  floor  18  ft.  square,  allowing  If  yards  for  waste  ? 

12.  How  many  sq.  yards  to  be  plastered  in  the  ceiling 
and  walls  of  a  room  26  by  20  ft.  and  12  ft.  high,  there  being 
3  windows  6  ft.  by  2  ft.  8  in.,  and  2  doors  8  by  3  ft.  ? 

13.  How  many  square  feet  of  boards  in  a  tight  fence  10 
rods  long  and  6  ft.  high  ? 

14.  How  many  sq.  rods  in  a  garden  231  ft.  long  and 
165  ft.  wide  ? 

15.  What  will  it  cost,  at  25/  a  sq.  foot,  to  construct  a 
slate  blackboard  34  ft.  3  in.  long  and  4  ft.  6  in.  wide  ? 


182  ARITHMETIC. 

1.  How  many  square  feet  in  6  boards  each  9  ft.  by  9  in.  ? 

2.  How  many  farms  of  16  acres  can  be  made  from  half 
a  square  mile  of  land  ? 

3.  A  lot  contains  l£  acres,  and  is  60  rods  long.     How 
wide  is  it  ? 

4.  How  many  square  inches  in  a  board  8  ft.  long  and 
9  in.  wide  ? 

5.  At  $5.80  per  square  rod,  what  will  £  of  an  acre  of 

land  cost  ? 

0 

6.  Find  the  square  contents  of  a  floor  21 J  ft.  long  and 
15J  ft.  wide. 

7.  Find  the  number  of   planks,  12  ft.  long  and  9  in. 
wide,  required  to  lay  a  floor  22  by  16  ft. 

8.  How  many  rolls  of  paper  24  ft.  long  and  Ij  ft.  wide 
will  be  needed  for  the  walls  of  a  room  28  by  24  ft.  and 
9  J  ft.  high,  no  allowance  for  openings  ? 

9.  What  will  the  paper  cost  at  $.37  J  per  roll  ? 

10.  How  many  yards  of  oil-cloth  f  of  a  yard  wide  will 
this  room  require  if  the  strips  run  lengthwise,  and  there  is 
a  waste  of  1  £  yards  for  matching  ? 

11.  What  will  the  oil-cloth  cost  at  $.25  per  yard? 

12.  How  many  yards  of  carpet  £  of  a  yard  wide  will  be 
required  for  a  room  24  ft.  long  and  18   ft.  wide,  if  the 
strips  run  lengthwise,  and  there  is  a  waste  of   9  in.  for 
matching  in  each  strip  ? 

13.  A  ceiling  25    X   30  ft.   contains   how  many  square 
yards  ? 

14.  What  is  the  difference  between  a  surface  of  6  square 
inches  and  one  6  inches  square  ? 

15.  What  is  the  cost  of  a  rectangular  field  40  rd.  wide 
and  92  rd.  long,  at  $63  an  acre  ? 

16.  How  many  square  inches  in  §  of  a  sq.  yard  ? 


REVIEW.  183 

1.  How  many  square  yards  to  be  plastered  in  a  room 
22  ft.  long,  20  ft.  wide,  10  ft.  high,  the  wainscoting  being 
3  ft.  high.,  deducting  100  sq.  ft.  for  openings  ? 

2.  How  many  bricks,  8x4  inches,  will  pave  a  walk  200 
ft.  long  and  1  rod  Avide  ? 

3.  What  will  be  the  cost  of  8  slate  blackboards  30  ft. 
by  3  ft.  4  in.,  at  25  cents  a  square  foot  ? 

4.  How  much  will  it  cost  to  lath  and  plaster  the  four 
walls  and  ceiling  of   a  room  20  ft.  long,  16  ft.  wide,  and 
10  ft.  high,  at  25  cents  a  square  yard  ?     No  allowance  for 
openings. 

5.  What  will  be  the  cost  of  carpeting  a  room  15f  ft. 
long  and  12£  ft.  wide,  with  carpet  f  yd.  wide,  at  a  dollar  a 
yard  ?  —  the  strips  to  run  from  side  to  side. 

6.  How  many  single  rolls  of  paper  will  be  required  to 
paper  the  walls  of  a  hall  80  ft.  long,  40  ft.  wide,  and  15  ft. 
high  ?  —  the  paper  to  be  18  inches  wide,  and  no  allowance 
for  openings. 

7.  At  $1.50  a  yard,  find  the  cost  of  a  carpet  27  inches 
wide,  for  a  room  15  ft.  by  12  ft.,  if  the  strips  run  length- 
wise, and  there  is  a  waste  of  £  of  a  yard  on  each  strip  for 
matching  ? 

8.  A  room  27  ft.  long  and  21  ft.  wide  is  to  be  carpeted 
with  carpet  a  yard  wide,  at  $1.25  a  lineal  yard.     Would 
the  cost  be  different  if  the  carpet  were  J  yd.  wide  at  $1.00 
a  yard,  and  how  much  ? 

9.  How  much  linoleum  will   be   required    to*  cover  a 
room  19  ft,  square,  and  what  will  it  cost  at  87 J/  a  square 
yard  ? 

10.  How  many  yards  of  carpet  f  yd.  wide  will  cover  a 
room  18  ft.  long  and  15  ft.  wide,  if  the  strips  run  the  long 
way  ?  the  short  way  ? 


184 


ARITHMETIC. 


Review.  —  Addition. 

The  following  table  shows  the  amounts  paid  for  teach- 
ers' salaries  in  the  Syracuse  schools  for  the  year  1893. 

Add  both  ways,  and*  make  the  sums  of  the  two  totals 
agree. 


SCHOOLS. 

SENIOK. 

JUNIOR. 

PBIMAKY. 

TOTAL. 

Salina  .     .     . 
Jefferson  . 
Genesee    . 
Prescott    .     . 
Seymour   .     . 
Putnam     .     . 
Irving  . 

$27972.13 

500.00 
4,469.54 
5,447.63 
4,038.51 

$1,800.38 
1,300.00 
2,349.38 
1,400.00 
2,060.25 
2,589.38 
2,282.76 

$2,110.50 
2,001.13 
2,574.13 
1,892.38 
2,962.13 
2,431.64 
2,533.63 

.     .     . 

Delaware  .     . 
Porter  .     .     . 
Gere     .     .     . 
Danforth  .     . 

425.00 
4,483.63 

2,293.00 
2,322.89 
1,849.69 
2,165.01 

2,&54.86 
3,919.50 
1,842.78 
2,230.95 

Brighton   .     . 
Rose 

3,446.56 

1,115.82 

1,749.63 
425  00 

Clinton      .     . 

2,774.39 

2  856  20 

Vine 

1  799  00 

Grace    . 

1,409.01 

3  160  71 

Merrick 

1,685.12 

2  319.69 

Madison    .     . 
Bassett      .     . 
Frazer  .     .     . 
Townsend 
Franklin   .     . 
May      .     .     . 
Montgomery  . 
Adams  . 

4,785.14 

3,352.51 

850.00 

2,493.13 
1,043.25 
2,320.20 
2,348.26 
2,846.25 
2,125.63 
2,542.89 
1,297.00 

2,249.00 
934.57 

2,472.78 
2,875.00 
4,704.40 
2,728.64 
4,413.45 
2  246  25 

... 

Asylum     .     . 
St.  Vincent    . 

1,498.75 
375.00 

550.00 

550.00 

.     .     . 

Total 

PARTS   OF    100  AND    1000.  185 

SHORT  MULTIPLICATION. 
Written  Work. 

1.  What  part  of  100  is  37|  ?  62£  ?  66|  ?  75  ?  87£  ? 

2.  What  part  of  1000  is  375  ?   625  ?  666|  ?  750  ?   875  ? 
How  much  is 

3.  |  of  100  |  of  1000 

4.  |  of  100  |  of  1000 

5.  §  of  100  §  of  1000 

6.  2  of  100  J  of  1000 

7.  J  of  100  I  of  1000 
8.    How  much  is  37  J  times  56  ? 

EXPLANATION.  —  37|  is   f  of  100,  therefore  37£  times 
56  is  |  as  much  as  100  times  56.     100  times  56  is  5600. 

700 
?.  of  WW  =  2100. 


To  multiply  by  37£,  annex  two  naughts  and  take  f  . 
Tell  how  to  multiply  by  33^,  25,  16|,  8J,  25,  50. 
Tell  how  to  multiply  by  62£,  66§,  75,  87£,  625,  666f  . 
Find  the  products  : 

9.  48  X  37£       19.   375  x  1128 

10.  64  x  37J       20.   648  X  375 

11.  72  x  37£       21.  625  x  888 

12.  88  X  62£       22.   723  X  625 

13.  96  X  62J       23.   272  x  666J 

14.  66§-  x  ise       24.  666|  x  189 

15.  66§  X  284       25.   750  X  948 

16.  288  X  75        26.   844  x  750 

17.  75  X  87        27.   112  x  875 

18.  96  X  87£       28.   328  X  875 


186  ARITHMETIC. 

Review.  —  Indicated  Work. 
Indicate,  and  find  the  result : 

1.  From  the  product  of  8  and  5,  diminished  by  the  quo- 
tient of  56  divided  by  8,  take  the  sum  of  11  and  3. 

2.  To  6  plus  the  product  of  8  and  9,  add  the  sum  of 
6  and  8  multiplied  by  9. 

3.  From  the  sum  of  5,  8,  and  11  take  the  sum  of  3,  6, 
and  4. 

4.  John  earned  70/  a  day,  but  was  obliged  to  pay  15/ 
for  lunch,  and  10/  for  carfare.     How  much  could  he  save 
daily  ? 

5.  A  man  bought  a  table  for  $20,  a  chair  for  $8,  and  a 
mattress  for  $6.    How  much  change  should  he  receive  from 
a  fifty-dollar  bill  ? 

6.  From  the  sum  of  6,  5,  and  4  take  the  difference  be- 
tween 20  and  30. 

(6  +  5  +  4)  -  (30  -  20) 

7.  To  the  difference  between  15  and  8,  add  the  difference 
between  11  and  16. 

8.  From  the  sum  of  11,  5,  and  6  diminished  by  4,  take 
the  difference  between  60  and  56. 

Add  and  prove : 

16  +  389  +  3684  +  38  = 
19  +  763  +  986  +  49  = 
28  +  982  +  428  +  76  = 
76  +  786  +  5963  +  95  = 
94  _|_  594  +  3694  +  87  = 
78  +  362  +  4896  +  63  = 
96  +  28  +  985  +  99  = 
89  +  9  +  8694  +  76  = 
96  +  364  +  9899  +  94  = 


BEVIEW.  187 

Mental  Work. 

Find  the  sum : 

1-   *  +  t                 5-      £  +  2£  9.     f +  f 

2.    i  +  t                  6.    1J  +  1J  10.      f  +  i 

3-  J  +  |                  ?•    2£  +  5£  11.      f  +  £ 

4-  T  +  T<y               8-      4  +  *  A  12-     I  +  A 
Find  the  difference  : 

13.  £  —  J                 17.    1J  -      i  21.      |  —  -J- 

14.  i  —  i                 18.    2^  —  1^  22.      I  —  i 

15.  £  _  i                 19.    3J  -      J  23.      f  —  T^ 

16.  £  —  |                  20.    1£  —  1}  24.  T\  —  ^ 

Find  the  product  in  simplest  form : 

25.  2  X  f                29.      i  of  f  33.  2  J  X  4 

26.  3  X  5                30.      f  of  £  34.  1J  X  6 

27.  J  X  4                31.      |  of  ^  35.  2|  X  3 

28.  |  X  3                32.      §  of  J  36.  !£  X  i 

Find  the  quotients  in  simplest  form  : 

37.  j  ^.  3               40.      i  -s-  2  43.      j.  -4-  5 

38.  j  -f-  4               41.      2  -T-  J  44.      $  -5-  £ 

39.  f  H-  7                42.      3  -f-  J  45.      ^  ^  £ 

46.  What  is  a  complex  fraction  ? 

47.  Change  examples  43  and  44  to  complex  fractions. 

Simplify : 


52. 


3  3 

49.    -  51.    |  t 

56.    Define  a  compound  fraction. 


188' 


AKITHMETIC. 


Written  Work. 

Find  the  sum  : 

1.    324|            2. 
25£ 
16* 

136 
297$ 

Subtract  : 

841 
163ft 

If 

.  16ft 

3.    $  14.15J               4. 
7.03 
112.19ft 

7.29} 

5.   384           16^ 

o        OQ    7 

5J       11.   253 

6.     28}  -     12g 

9.    16J 

-  11J       12.      15£  - 

7.    163J  -  129J 

10.    28J 

-    4J       13.      11    - 

28J 


20J 

19* 

28J 


-     5J 


Find  the  product : 

14.  126}  X  6  17.    182  X  5J-  20.    28$ 

15.  1586|  X  3  18.      66  X  2j  21.      3| 

16.  2894f  X  7  19.      38  X  7|  22.    17§ 

Find  the  quotients : 

23.  §)1824  26.    6)1352^  29.    28^ 

24.  5^)1856  27.    7)1892$  30.    15} 

25.  |)18934  28.    8)1624§  31.      1^ 
Simplify : 

QO         -*-*^^"  QK                  7?  QQ              O 

OA.       -  OO.       OO.       

7  6                               % 

33.  ?i  36.    ?4  39.    i 

41  4J                                  7J 

34.  A  37.    —  40.    ^ 

5}  f                                   5 

41.  }  of  if  of  ft  ~  ft  of  T\  of  f . 

42.  Add  }  of  5i  and  f  of  5£  of  J. 


X  7f 
X  5J- 

X  5J 

-i-  2| 


REVIEW. 


189 


1.    Express  by  figures,  three  million,  twenty-five  thou- 
sand, three  hundred  eight. 

Separate  into  groups  and  read : 

2.  36948006         5.        9984321  8.    3890000 

3.  5000609         6.   300500200  9.   2503001 

4.  2890006        7.       2983261  10.   2863259 

11.  Express  the  number  of  this  year  in  Roman  Notation. 
Read  and  add : 

12.  $369.842     13.    $369.56      14.  $  .39      15.    $394.634 

25.053                26.03  .384               28.52 

695.06                    9.565  .06                   3.216 

298.065                28.696  1.103               53.698 

694.01                239.001  .582               21.034 

986.959              598.091  .98               500.005 

16.  ReadLXXXI;  CCCCXCI;  DCLXXXIX. 

17.  165  +  16  X  5  +  ?  =  395. 

18.  384  +  64  -v-  8  -  ?  =  250. 

19.  (384  +  64)  -r-  8  -  45  =  ? 

20.  (384  +  64)^8x6-58x4=? 

21.  384  +  64  -r-  8  X  6  -  58  X  4  =  ? 
Rapid  subtraction,  without  copying. 

22.  500000     25.  568594        28.    3695.286 
6852683       965989  56397.01 

23. 


389648 
95999 

24.   3000530 
29856331 


26.  $  3984.325 
53681.20 


29.  $  7787.10 
2999.999 


27. 


$3698 
299.598 


30.  Multiply  589635  by  286  ;  by  3950  ;  by  90006. 

31.  Divide,  without  copying  : 

369081  by  9  ;  by  10  ;  by  11  ;  by  12.     Add  the  quotients. 


190  ARITHMETIC. 

Indicate  the  operations  and  find  results : 

1.  To  the  product  of  5  and  6,  add  5,  and  divide  the 
sum  by  fourteen  minus  seven. 

2.  From  65  subtract  the  quotient  of  60  divided  by  five, 
and  add  three. 

3.  Thirty  plus   twenty-five   minus   twenty-three   multi- 
plied by  three. 

4.  Six  times  nine,  minus  seven  times  seven. 

5.  46  minus  16  plus  10,  divided  by  three. 

6.  35  plus  15  minus  the  quotient  of  14  divided  by  9. 

7.  35  times  4,  minus  14  plus  16. 

8.  Multiply  the    quotient  of   56  divided  by  14  by  12, 
and  subtract  12  from  the  product. 

(56  -^  14)  X  12  -  12  ;  or  [(56  ~  14)  X  12]  -  12 ;  or  f  f 

X  12  -  12. 

I 

NOTE.  —  Explain  use   of   brackets,  and  horizontal  vin- 
culum. 

9.  3  fourths  of  80,  plus  the  sum  of  25  and  16. 
Eead,  and  find  results  : 

1.   What  is  the  value  of  (22  +  8  +  16)  X  (18  +  10  +  21) 
divided  by  (9  +  5  +  7)  X  (15  +  8). 


2.  (56  +  4  -v-  12)  x  (15  -  7)  =  ? 

3.  25  -  13  +  10  -r-  10  =  ? 

4.  (125  +  75)  X  6  +  36~3  -  92  =  ? 

5.  (28  -  7)  X  6  +  (92  +  7)  -^  9  -  86  +  10  -f-  12. 

6.  2x4x8x13x7x16  divided  by  26  X  14  X 
8  =  ? 

7.  Multiply  by  6  the  quotient  of  72  divided  by  12,  and 
subtract  6  from  the  product. 


EEVIEW. 


191 


8.  f  = 

9.  15  = 

10.   A  = 


Mental  Work. 

1 .  In  f ,  how  many  twentieths  ? 

2.  How  many  sixths  in  f  of  a  mile  ? 

Reduce 

3.  f  to  9ths. 

4.  |  to  24ths. 

5.  5f  to  6ths. 

6.  £  to  24ths. 

To  lowest  terms : 

19-  if 

20.  if 

21.  if 

22.  M 

To  improper  fractions : 

35.  7£  39.      5] 

36.  9£  40. 

37.  14^  41. 

38.  2A  42. 


11.  IJtoSths. 

12.  2J  to  20ths. 

13.  4  to  25ths. 

14.  1    to  16ths. 


15.  if 

16.  if 

17.  if 
18. 


23.    U 

27.    -|f 

31. 

24.    |^ 

28.    Jft 

32. 

25.    §| 

29.    4«* 

33. 

26.    3ft 

30.    J-gg 

34. 

43.    12f 

47.    12^ 

44.    11^ 

48.    313 

45.       6^ 

49.    10T9- 

46.       3| 

50.    20| 

To'  integers  or  mixed  numbers  : 


51. 
52. 
53. 
54. 


V 
V 


55. 
56. 
57. 
58. 


59.  |f 

60.  fft 

61.  Yr 

62.  M^ 


63. 
64. 
65. 
66. 


To  a  common  denominator  : 

67.  |,  J  69.    i,J  71. 

68.  |,  |  70.    i,  f  72. 

73.  Add  i  and  £  ;  |  and  }  ;  i,  £,  and  J. 

74.  Multiply  |  by  |  ;  f  by  f  ;  f  by  J. 


J, 


192  ARITHMETIC. 

• 

Oral  Work. 

1.  If  a  man  spends  J  of  a  dollar  each  day,  how  many 
dollars  will  he  spend  in  11  days  ? 

2.  If  a  bushel  of  apples  cost  $1.24,  what  will  a  peck 
cost? 

3.  5  is  J  of  what  number  ? 

4.  5  is  |  of  what  number  ? 

5.  If  it  costs  37£  cents  a  week  for  milk  tickets,  what 
will  it  cost  for  8  weeks? 

6.  4  is  3  times  what  number  ? 

7.  4  is  J  of  what  number  ? 

8.  If  6  is  |  of  some  number,  what  is  £  ?     J  ? 

9.  Add  f  and  A;  §  and  f ;  $  and  ft? 

10.  3  is  |  of  what  number  ? 

11.  What  is  the  difference  between  £  and  J  ? 

12.  How  many  eighths  does  it  take  to  make  one-half? 
How  many  GOths  in  J  ? 

13.  How  many  times  12  are  3  times  8  ? 

14.  \  of  28  are  how  many  times  2  ? 

15.  If  3  oranges  cost  lo/,  what  will  2  oranges  cost  ? 

16.  If  5  apples  cost  2  cents,  what  will  1  apple  cost  ? 
What  will  8  apples  cost  ?     How  many  can  I  buy  for  8 
cents  ? 

17.  A  boy  spent  6  cents,  which  was   }  of  all  he  had. 
How  much  had  he  ?     (Question.) 

18.  If  3  men  do  a  piece  of  work  in  5  days,  how  long  will 
it  take  one  man  to  do  it  ? 

19.  A  boy  who  had  \  of  an  apple  gave  away  one-half  of 
what  he  had.     What  part  of  the  apple  did  he  give  away  ? 

20.  i  of  f  —  f  of  \  =  ? 

21.  9  is  {  of  what  number  ? 


REVIEW.  193 

Indicated  Work. 

Indicate  and  cancel : 

1.  How  many  sq.  yards  of  carpeting  in  a  floor  24  ft. 
long  and  18  ft.  wide  ? 

2.  How  many  acres  in  a  field  140  rods  long  and  80  rods 
wide  ? 

3.  What   will   be  the  cost  of  1632  quarts  of  nuts  at 
$2.50  a  bushel  ? 

NOTE.  —  In  cancellation,  it  is  convenient  to  change  cents 
to  the  fraction  of  a  dollar,  thus,  40/  =  $f,  37£/  ==  $f, 
$2.50  =  $2J,  etc. 

4.  At  6/  a  quart,  how  many  gallons  of  cider  can  be 
bought  for  $4.80  ? 

5.  30  pounds  of  steel  will  make  how  many  horse  shoes, 
each  weighing  6  ounces  ? 

6.  In  what  time  can  a  boy,  at  60/  a  day,  earn  as  much 
as  a  man  can  earn  in  40  days  at  $3.00  a  day  ? 

7.  What  will  it  cost  to  paint  8  blackboards  each  18  ft. 
long  and  3  ft.  wide,  at  40/  a  sq.  yard  ? 

8.  A  man  sold  15|  cords  of  wood  at  $8^  a  cord,  and 
received  payment  in  wheat  at  $J  a  bushel.     How  many 
bushels  of  wheat  did  he  receive  ? 

9.  If  2£  yards  of  cloth  cost  $10,  what  will  J  of  a  yard 
cost? 

10.  If  8  bushels  of  wheat  cost  $6,  how  many  bushels 
can  be  bought  for  $!•£  ? 

11.  If  3J  Ib.  of  tea  cost  $2J,  what  will  f  of  a  pound 
cost? 

12.  A  garden  is  3  rods  wide  and   10  rods   long.     How 
many  3  foot  paces  will  a  man  take  in  going  around  it  ? 

13.  How  many  boards  1  ft.  wide  and   12  ft.  long  will 
it  take  for  a  tight  fence  5  ft.  high  and  50  ft.  long  ? 


194 


ARITHMETIC. 


CUBIC  MEASURE. 

A  Solid  is  anything  that  has  length,  breadth,  and  thick- 
ness. 

A  Rectangular  Solid  is  a   body  having  six  rectangular 
sides  or  faces. 

A  Cube  is  a  body  having  six  square  sides  or  faces. 

Every  cube  is  a  rectangular  solid,  but  every  rectangular 
solid  is  not  a  cube. 

A  cubic  inch  is  a  cube  1  inch  long,  1  inch  wide,  and  1 
inch  thick. 

A  cubic  foot  is  a  cube  1  ft.  long,  1  ft.  wide,  and  1  ft. 
thick. 

A  cubic  yard  is  a  cube  1  yd.  long,  1  yd.  wide,  and  1  yd. 
thick. 

The  Volume  or  Solidity  of  a  body  is  the  number  of  cubic 
units  that  it  contains. 

How  many  cubic  inches  in  a  block  4  inches  long,  3  inches 
wide,  and  2  inches  thick  ? 

The  block  is  made  up 
of  two  layers,  each  1  in. 
thick.  In  the  top  layer 
there  are  4  times  3  cu. 
inches.  In  the  two  layers 
there  are  2  X  (4  X  3  cu. 
in.)  =  24  cu.  inches. 

To  find  the  volume  or 
solid  contents  of  a  rect- 
angular solid,  obtain  the 
product  of  the  length, 
breadth,  and  thickness. 

NOTE.  —  The  three   dimensions    must   be   of   the   same 
denomination. 


3  IN.  WIDE 


10 


CUBIC   MEASURE.  195 

1.  How  many  cubic  inches  in  a  block  12  inches  long,  6 
inches  wide,  and  4  inches  thick  ? 

2.  What  is  the  volume  of  a  block  of  marble  6  ft.  long, 
5  ft.  wide,  and  4  ft.  thick  ? 

3.  What  is  the  volume  of  6  bricks,  each  being  8  by  4 
by  2  inches  ? 

4.  The  solid  contents  of  a  block  are  720  cubic  feet.     It 
is  10  ft.  high  and  9  ft.  wide.     How  thick  is  it  ? 

To  find  one  dimension  when  the  solidity  and  the  other 
two  dimensions  are  known,  divide  the  solidity  by  the 
product  of  the  two  given  dimensions. 

TABLE    OF  CUBIC  MEASURE. 

1728  cubic  inches  =  1  cubic  foot  (cu.  ft.). 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.). 
16  cubic  feet  =  1  cord  foot  (cd.  ft.). 
8  cord  ft.  or  128  cu.  ft.  =  1  cord  (cd.). 

5.  A  cord  of  wood  is  8  ft.  long,  4  ft.  wide,  and  4  ft. 
high.     How  many  cubic  feet  does  it  contain  ? 

A  cord  foot  is  J  of  a  cord. 

It  is  4  ft.  high,  4  ft.  wide,  and  1  ft.  long. 

8  of  these  placed  together  make  a  cord. 

NOTE.  —  Illustrate,  using  8  books  of  equal  size. 

6.  Prove  that  there  are  1728  cu.  inches  in  a  cu.  foot. 

7.  Prove  that  there  are  27  cu.  ft.  in  a  cubic  yard. 
Keduce  to  cubic  inches  : 

8.  11  cu.  ft.  145  cu.  inches.         11.    1  cord  8  cu.  ft. 

9.  38  cu.  ft,  1046  cu.  inches.       12.    3  cords  150  cu.  in. 
10.    4  cu.  yards  15  cu.  feet.  13.    1  cord  foot. 
Reduce  to  higher  denominations  : 

14.  498326  cu.  in.  16.    369426  cu.  in. 

15.  269842  cu.  in.  17.    846394  cu.  in. 


196  ARITHMETIC. 

Reduce  to  lower  denominations  : 

18.  J  cu.  yd.  20.    16  cu.  yd.  5  cu.  ft. 

19.  |  cu.  yd.  21.    ]  cu.  yd. 

22.  18  cu.  yd.  3  cu.  ft.  159  cu.  in. 

23.  15  cords  14  cd.  ft. 

24.  J  cu.  ft. 

25.  78  cu.  yd. 

26.  6  cu.  yd.  6  cu.  ft.  6  cu.  in. 

27.  14J  cu.  yd. 

28.  What  part  of  a  cu.  yard  is  2  cu.  feet.     (Question.) 

A  cubic  yard  =  27  cu.  ft. 
The  question  then  becomes,  — 
What  part  of  27  cu.  ft.  is  2  cu.  ft.  ? 

29.  What  part  of  a  cubic  foot  is  144  cubic  inches  ? 

30.  What  part  of  a  cubic  yard  is  144  cubic  inches  ? 

31.  A  cubic  inch  is  what  part  of  a  cubic  foot  ? 

32.  2  cord  feet  are  what  part  of  a  cord  ? 

33.  What  will  be  the  cost,  at  20/  a  cubic  yard,  to  dig 
a  cellar  45  ft.  long,  36  ft.  wide,  and  5 J  ft.  deep  ? 

34.  Reduce  |  of  a  cu.  foot  to  a  fraction  of  a  cu.  yard. 

35.  What  is  the  cost  of  a  block  of  granite  6  ft.  6  in.  long, 
4  ft.  3  in.  wide,  and  3  ft.  thick,  at  $15.75  a  cubic  yard  ? 

36.  What  is  the  difference  between  5  cubic  inches  and  a 
cube  5  inches  on  each  edge  ? 

37.  How  many  cubic  feet  in  a  cube  two  feet  on  each 
edge  ?     How  many  cubic  inches  ? 

38.  What  is  the  capacity  in  cubic  feet  of  a  dry-goods  box 
3  ft.  by  2J  ft.  by  2  f t  ? 

39.  How  many  2-in.  cubes  can  be  cut  from  a  block  of 
marble  2  ft.  long,  18  in.  wide,  and  15  in.  thick  ? 


CAPACITY.  197 

Capacity  of  Cisterns. 

1.  A  wine  gallon  fills  231  cubic  inches  of  space.     How 
many  gallons  will  fill  a  cubic  foot  of  space  ? 

J^T8-  =  about  7|  gallons.     Ans. 

NOTE.  —  It  is   sufficiently  accurate  in  estimating  large 
liquid  capacities  to  reckon  1\  gal.  to  the  cubic  foot. 

2.  A  cistern  is  5  ft.  square  and  6  ft.  deep.     How  many 
gallons  of  water  will  it  contain  ? 

Solve  both  ways  and  note  the  difference. 

3.  What  is  the  capacity  in  barrels  of  the  cistern  in 
Ex.  2? 

4.  How  many  barrels  of  water  in  a  cistern  7  ft.  long, 
4£  ft.  wide,  and  5 £  ft.  deep  ?     (Indicate  and  cancel.) 

5.  What  is  the  capacity  in  barrels  of  a  tank  3  ft.  by 
4£  ft.  and  4f  ft.  deep  ? 

6.  How  many  gallons  of  water  in  a  tank  whose  capacity 
is  150  cubic  feet  ? 

7.  How  many  cubic  feet  in  a  cistern  that  will  hold  1500 
gallons  of  water  ? 

Capacity  of  Bins. 

8.  A  bushel  fills  2150.42  cubic  inches  of  space,  which 
is  l£  cu.  ft.,  nearly. 

NOTE.  —  In  estimating  large   quantities  of  grain,  it  is 
sufficiently  accurate  to  reckon  \\  cu.  ft.  to  the  bushel. 

9.  How  many  bushels  of  grain  will  a  bin  hold  that  is 
6  ft.  long,  5  ft.  wide,  and  4  ft.  deep  ?    (Indicate  and  cancel.) 

Solve  both  ways  and  note  the  difference. 

10.  How  many  bushels  in  a  bin  that  contains  150  cubic 
feet? 

11.  How   many   cubic    feet    in   a   bin   that   holds    150 
bushels  ? 


1 98  ARITHMETIC. 

Kead  and  add  : 

1.    36,942,006  2.    $69804.41 

2,000,052  306.005 

3,540,004  2904.046 

81,569,298  198.36 

1,005,000  2940.265 

3.  How  many  bushels  of  oats  at  55/  a  bushel  can  be 
bought  for  $52.25? 

4.  The  divisor  is  36846,  the  quotient  515,  the  remainder 
1658.     What  is  the  dividend  ? 

5.  Bought  356  bbl.  of  flour  at  $6.50  a  barrel,  and  sold 
the  whole  for  $2198.50.     How  much  did  I  gain  or  lose  ? 

6.  A  newsboy  buys  96  papers  a  day  at  18/  a  dozen,  and 
sells  them  at  3/  each.     How  much  money  has  he  made  at 
the  end  of  a  week  if  he  has  16  old  papers  left  ? 

7.  How  many  square  yards  in  a  pavement  348  ft.  long 
and  6  ft.  wide  ? 

Write  results  without  copying : 

8.  89742  --    9  12.    2189362  -=-    482 

9.  168439  -f-  12  13.   3698452  -^  1962 

10.  486982  x    9  14.    2893004  -^-  1009 

11.  290006  x    8  15.   3698421  +  2196 
16.    From  6990026  17.    Take      36984 

Take      980059  From  161103 

18.    Take    38948 
From  94321 

19.  How  many  tiles  12  in.  by  6  in.  will  it  take  to  cover 
a  hearth  3  ft.  wide  and  6  ft.  long  ?     (Diagram.) 

20.  If  an  acre  of  wheat  yields  30  bushels,  how  much  will 
a  field  yield  that  is  25  rd.  long  and  45  rd.  wide  ? 


MISCELLANEOUS    TABLES.  199 

MISCELLANEOUS    TABLES. 

12  units  or  things,  1  dozen,  (doz.). 

12  dozen,  1  gross,  (gro.). 

20  units,  1  score. 
196  lb.,  1  barrel  of  flour. 
200  lb.,  1  bbl.  of  beef,  pork,  or  fish. 
280  lb.,  1  barrel  of  salt. 

PAPER. 

24  sheets,     1  quire. 
20  quires,     1  ream. 
2  reams,     1  bundle. 
5  bundles,  1  bale. 
Oral  Work. 

1.  How  many  are  3  gross  of  pencils  ? 

2.  What  is  the  cost  of  J  gross  of  pens  at  60/  a  gross  ? 

3.  How  many  are  3  score  years  ? 

4.  How  many  are  3  score  and  10  years  ? 

5.  How  many  are  5  dozen  eggs  ?  6 J  dozen  eggs  ? 

6.  How  many  sheets  in  3  quires  of  paper  ? 

7.  How  many  quires  in  £  a  ream  ? 

8.  84  eggs  are  how  many  dozen  ? 

9.  How  many  reams  in  a  bale  of  paper  ? 

10.  How  many  pounds  in  J  bbl.  of  flour  ? 

11.  How  many  pounds  in  £  bbl.  of  salt  ? 

Written  Work. 

12.  How  many  dozen  in  66  cucumbers  ? 

13.  What  is  the  cost  of  6  quires  of  paper  at  $4  a  ream  ? 

14.  What  will  8  gross  of  copy  books  cost  at  10/  apiece  ? 
16.    If  paper  is  bought  at  $2  a  ream  and  sold  at  18/  a 

quire,  what  is  the  gain  on  6  reams  ? 


200  ARITHMETIC. 

TIME. 

60  seconds,  1  minute,  (min.). 
60  minutes,  1  hour,  (h.). 
24  hours,  1  day,  (da.). 

365  days,  1  common  year,  (y.). 

366  days,  1  leap  year. 
Also: 

7  days,  1  week  (wk.). 
12  months  (mo.),  1  year. 
100  years,  1  century. 

The  solar  year  is  365J  days,  nearly. 

For  convenience  365  days  is  taken  for  a  common  year. 
The  .£  day,  in  4  years,  amounts  to  another  day,  making 
every  4th  year  366  days.  This  is  called  leap  year.  This 
extra  day  is  added  to  February. 

Days  in  each  month  : 

January  31  days.  July  31  days. 

February  28  or  29  days.  August  31  days. 

March  31  days.  September  30  days. 

April  30  days.  October  31  days. 

May  31  days.  November  30  days. 

June  30  days.  December  31  days. 

Oral  Work. 

1.  How  many  minutes  in  2  hours  ?  ^  hour  ?  2J  hours  ? 

2.  Reduce  to  hours :    180  minutes ;    120  minutes ;    30 
minutes. 

3.  How  many  hours  in  a  week  ? 

4.  How  many  days  in  March  and  June  ? 

5.  What  4  months  have  30  days  ? 

6.  How  many  have  all  the  rest  except  February  ? 

7.  What  part  of  an  hour  is  45  minutes  ?     (Question.) 


TIME.  201 

Written  Work. 

Reduce  to  lower  denominations  : 

1.  15  min.  29  sec.  5.    3  wk.  4  da.  6  min. 

2.  16  da.  16  hr.  6.    f  of  a  day. 

3.  15  da.  6  hr.  7.    £  of  a  day. 

4.  3  wk.  11  hr.  8.    5£  weeks. 
Reduce  to  higher  denominations  : 

9.  1565  sec.  13.  359642  sec. 

10.  3246  min.  14.  29843  hr. 

11.  3694  h.  15.  3000  min. 

12.  56984  sec.  16.  300000  hr. 

17.  lleduce  J   of   an  hour  to   the    fraction  of   a  day  ? 
(Question.) 

18.  What  part  of  a  week  is  J  of  a  minute  ?     (Question.) 

19.  How  many  weeks  in  July,  August,  and  September  ? 

20.  If  a  boy  walk  J  mile  in  10  minutes,  how  long  will  it 
take  him  to  walk  16  miles  ? 

21.  How  many  days  from  the  4th  of  May  to  the  4th  of 
July? 

22.  How  many  hours  in  the  month  of  August  ? 

The  Winter  months  are  December,  January,  and  February. 
The  Spring  months  are  March,  April,  and  May. 
The  Summer  months  are  June,  July,  and  August. 
The  Autumn  months  are  September,  October,  November. 

23.  Which  is  the  shortest  season  ?     Why  ? 

24.  Is  it  the  shortest  in  leap  year  ? 

25.  How  many  more  days  in  this  year  ? 

26.  If  a  man  earn  \fl  a  minute,  what  will  he  earn  in  a 
day  of  8  hours  ? 

27.  If  a  clock  loses  \  a  second  every  day,  how  much  will 
it  lose  in  the  summer  months  ? 


202  ARITHMETIC. 

Reduce  to  lower  denominations : 

1.  48  Ib.  12  oz.  to  ounces. 

2.  15  cwt.  90  Ibs.  to  pounds. 

3.  15  Ib.  7  oz.  14  dr.  to  drams. 

4.  3  gal.  3  qt.  1  pt.  to  pints. 
6.    4  bbl.  4  gal.  to  pints. 

6.  4  qt.  3  pt.  3  gi.  to  gills. 

7.  4  bu.  3  pk.  6  qt.  to  quarts. 

8.  2  bu.  2  pk.  2  qt.  1  pt.  to  pints. 

9.  16  bu.  4  qt.  to  pints. 

10.  £  ton  to  pounds. 

11.  J  hhd.  to  quarts. 

12.  6J  gal.  to  gills. 

13.  J  bushel  to  quarts. 
Eeduce  to  higher  denominations : 

14.  2698  dr.  to  pounds,  etc.  21.  2180  pt.  to  bushels,  etc. 

15.  4694  oz.  to  pounds,  etc.  22.  3694  pk.  to  bushels. 

16.  4924  Ib.  to  tons,  etc.  23.  3  oz.  is  what  part  of  1  Ib.? 

17.  2946  pt.  to  hhd.,  etc.  24.  4  pt.  is  what  part  of  1  gal.? 

18.  3694  gi.  to  gal.,  etc.  25.  4  qt.  is  what  part  of  1  bu.? 

19.  3314  pints  to  gal.,  etc.  26.  J  pk.  is  what  part  of  2  pk.? 

20.  734  qt.  to  bushels.  27.  3  pk.  is  what  part  of  3  bu.? 

28.  How  many  times  can  a  2-quart  pail  be  filled  from  a 
half -bushel  of  chestnuts  ? 

29.  A  man  bought  sweet  potatoes  at  $2  a  bushel,  and 
sold  them  at  70/  a  pk.     What  did  he  gain  on  3  bu.  ? 

30.  If  vinegar  retails  at  1|/  a  pint,  what  will  a  barrel  of 
vinegar  sell  for  ? 

31.  From  a  barrel  of  wine  f  was  sold  in  one  day,  and  \  in 
another.     How  many  quarts  are  left  ? 


CUBIC    MEASURE.  203 

1.  How  high  is  a  room  that  is  24^  ft.  long,  20  ft.  wide, 
and  contains  4410  cubic  feet  ? 

2.  How  long  a  building  that  is  10  ft.  wide  and  8  ft. 
high  will  it  require  to  hold  10  cords  ? 

3.  A  pile  of  wood  4  ft.  long.  4  ft.  wide,  and  4  ft.  high, 
will  cost  how  much  at  $4.50  a  cord  ? 

4.  How  many  cubic  inches   of  space  in  a  box  10   in. 
long,  6  in.  wide,  and  4  in.  high  ? 

5.  What  part  of  a  cubic  yard  is  the  space  in  this  box  ? 

6.  The  volume  of  a  rectangular  solid  is  1200  cu.   ft. 
It  is  20  ft.  long  and  4  ft.  high.     How  wide  is  it  ? 

7.  A  piece  of  marble  16  ft.  long,  12  ft.  wide,  and  9  ft. 
thick  can  be  sawed  into  how  many  blocks  of  a  cubic  foot 
each? 

8.  What  will  it  cost  to  make  an  embankment  contain- 
ing 54270  cu.  ft.  of  earth  at  $.15  a  cubic  yard  ? 

9.  At  $6.40  a  cord,  hqw  much  money  will  pay  for  a  pile 
of  wood  80  ft.  long,  32  ft.  wide,  and  12  ft.  high  ? 

10.  Find  the  number  of  cubic  inches  in  a  piece  of  ice  3 
ft.  long,  2 J  ft.  wide,  and  18  inches  thick  ? 

11.  How  many  cords  of  wood  may  be  piled  in  a  shed  62 
ft.  long,  20  ft.  wide,  and  12  ft.  high  ? 

12.  What  is  the  difference  between  6  cubic  inches  and  a 
6-inch  cube  ? 

13.  If  300  cu.  ft.  of  breathing  space  is  required  for  a 
pupil,  how  many  pupils  should  be  seated  in  a  schoolroom 
30  ft.  square  and  10  ft.  high  ? 

14.  How  many  cubic  yards  of  earth  will  be  removed  in 
digging  a  cellar  36  ft.  square  and  6  ft.  deep  ? 

15.  How  many  books  9  in.  by  6  in.  by  1^  in.  can  be 
packed  into  a  chest  4  ft.  by  2  ft.  by  1^  ft.  ?     (Indicate  and 
cancel.) 


204  ARITHMETIC. 

16.  How  many  cubic  feet  of  snow  on  18  square  feet  of 
ground,  the  snow  being  9  inches  deep  ? 

17.  How  many  bricks,  8x4x2  inches,  will  it  take  to 
build  a  wall  16  x  8  x  1 J  ft  ?     (Cancel.) 

18.  How  many  cubic  inches  in  a  stick  of  timber  1  foot 
square  at  the  ends  and  8  ft.  long  ? 

19.  How  many  cubic  feet  of  air  in  a  room  16  ft.  8  in. 
long,  12  ft.  9  in.  wide,  and  8  ft.  4  in.  high  ? 

20.  How  many  2-in.  cubes  may  be  made  from  a  piece  of 
wood  6  by  4  by  2  ft.? 

21.  How  many  loads  of   earth,  each  load  containing  a 
cubic  yard,  in  an  excavation  30  ft.  long,  26  ft.  wide,  and  14 
feet  deep  ? 

22.  How  many  cubic  inches  in  3  barrels,  there  being  231 
cubic  inches  in  a  gallon  ? 

23.  A  cubic  yard  of  earth  makes  a  load.      How  many 
loads  must  be  excavated  for  a  cellar  32  ft.  long,  30  ft. 
wide,  and  6J  ft.  deep  ? 

24.  A  brick  is  8  in.  long,  4  in.  wide,  and  2  in.  thick. 
How  many  will  it  take  to  build  a  wall  30  ft.  long,  20  ft. 
wide,  and  1 J  ft.  thick,  using  no  mortar  ? 

25.  A  vat  is  4  ft.  long,  3  ft.  wide,  and  6  ft.  9  in.  deep. 
How  many  gallons  of  oil  will  it  hold  ? 

26.  How  many  bricks,  8  by  4  by  2  in.,  will  be  needed  to 
build  a  wall  16  ft.  long,  4  ft.  high,  and  1  ft.  thick  ?     (Use 
cancellation.) 

27.  How  many  blocks  8  in.  long,  6  in.  wide,  and  1  in. 
thick,  can  be  packed  into  a  box  2  ft.  by  1J  ft.  by  lj  ft  ? 
(Use  cancellation.) 

28.  A  pile  of  wood  is  32  ft.  long,  12  ft.  high,  and  8  ft. 
wide.     How  much  will  it  cost  at  $3.37^  a  cord  ? 

29.  A  cord  foot  is  what  part  of  a  cord  ? 


MEASUREMENTS.  205 

30.  How  many  cubic  feet  of  water  will  a  trough  hold 
that  is  6  ft.  long,  2  ft.  wide,  and  18  in.  deep  ? 

31.  How  many  cubic  feet  of  air  in  a  room  18  by  15  by 
10  ft.  ? 

32.  How  many  cords  of  wood  in  a  pile  32  ft.  long,  8  ft. 
high,  and  4  ft.  wide  ?     (Use  cancellation.) 

33.  There  are  231  cubic  inches  in  a  gallon.     How  many 
gallons  will  a  tank  hold  that  is  6  ft.  by  6  ft.  and  2  ft. 
deep? 

34.  A  and  B  are  1,000  miles  apart  and  travel  towards 
each  other,  A  at  the  rate  of  90  miles  a  day  and  B  at  the 
rate  of  80  miles  a  day.     In  how  many  days  will  they  meet  ? 

35.  A  square  mile  of  land  may  be  cut  up  into  how  many 
80-acre  farms  ?     (Diagram.) 

36.  In  the  above  problem  what  will  be  the  dimensions  of 
each  farm  ? 

37.  An  ordinary  brick  is  8  in.  by  4  in.  by  2  in.     How 
many  sq.  inches  of  paper  will  exactly  cover  it  ? 

38.  Make  a  diagram  on  thick  paper,  cut,  and  fold  into 
the  form  of  a  brick. 

39.  A  chest  is  4  ft.  long,  2  ft.  wide,  and  2£  ft.  high. 
How  many  yards  of   cloth  will  be  required  to  cover  all 
sides  except  the  bottom,  allowing  ^  yd.  for  laps.     (Diagram.) 

40.  Which  will  hold  the  more  water,  a  can  6  in.  by  4  in. 
by  3  in.,  or  a  can  in  the  form  of  a  4-inch  cube  ? 

41.  How  many  bricks,  8  by  4  by  2  in.,  will  fill  1  cubic 
foot  of  space  ?     (Factor  and  cancel.) 

42.  How  many  bricks  in  a  pile  10  ft.  long,  8  ft.  wide, 
and  9  ft.  high  ? 

43.  At  $.87^  a  bushel,  what  will  be  the  cost  of  the 
wheat  that  can  be  contained  in   a  bin  15  ft.  long,  12  ft. 
wide,  and  4  ft.  high  ? 


206  ARITHMETIC. 

Questions  of  Relation.  —  Oral  Work. 
What  part  of 

1.  7  is  5  ?  6.    14  is  8  ?  11.    16  is  4  ? 

2.  11  is  6  ?  7.  25  is  15  ?  12.  28  is  14  ? 

3.  13  is  8  ?  8.  36  is  24  ?  13.  15  is  7£  ? 

4.  16  is  15?  9.  27  is  18?  14.  30  is  8  ? 

5.  21  is  11  ?  10.  19  is  18  ?  15.  42  is  6  ? 

Form  the  other  questions  from  the  first  five  of  the  above. 
Of  what? 

1.  12  is  J         4.      6  is  I         7.   25  is  g         10.    15  is  J 

2.  16  is  §         5.    18  is  §         8.    36  is  f         11.      9  is  ft 

3.  11  is  |         6.    14  is  }         9.    24  is  f         12.      7  is  J 
Write  problems,  using  the  first  five  of  the  above. 

How  much  is 

1.  f  of  25  ?     4.    |  of  60  ?     7.    f  of  9  ?       10.    ^  of  28  ? 

2.  I  of  36  ?      5.    }£  of  24  ?    8.    |  of  45  ?      11.    f  of  35  ? 

3.  |  of  48  ?      6.    f  of  14  ?      9.    ft  of  16  ?  12.    f  of  42  ? 
From  the  first  five  of  the  above  form  the  other  questions. 

Written  Work. 

1.  What  part  of  15  is  3J  ? 

2.  What  part  of  15f  is  6  ? 

3.  f  is  what  part  of  f  ? 

4.  2|  is  what  part  of  5J  ? 

5.  381  is  T9o  of  what  ? 

6.  §  is  f  of  what  ? 

7.  224  is  |f  of  what  ? 

8.  2 1  is  f  of  what  ? 

9.  How  much  is  T97  of 


REVIEW.  207 


Written  Work. 

Add  both  ways.     Prove  by  adding  sums. 

1.    684  +  396  +    28  +  934  +  287 

399  +  763  +  198+    26+    32 

39  +    63  +  984  +  699  +  721 

897  +  673  +  987  +  38  +  489 

394  +  998  +  483  +  976  +  694 

21  +   8  +  64  +  16  +  114 

371  +  973  +  163  +  814  +  748 

29  +    28  +    63  +  982  +    36 


Multiplication. 

2. 

395  x 

382 

7. 

3983 

X 

4i 

12. 

369§ 

X 

6 

3. 

786  X 

25 

8. 

26984 

X 

3£ 

13. 

263J 

X 

15 

4. 

3985  X 

683 

9. 

2634 

X 

6* 

14. 

394| 

X 

14 

5. 

2963  X 

29 

10. 

2835 

X 

45 

15. 

784f 

X 

14 

6. 

876  X 

250 

11. 

3892 

X 

5J 

16. 

298| 

X 

8 

Subtraction. 

17. 

36983 
4999 

18. 

2984 
46321 

19. 

3685f 
_398| 

20.  264f 
5983^ 

Division. 

21.  3985  -5-  185        24.      269  -f-  36|        27.    29|  -f- 

22.  3553  -T-  13|        25.    2896  -f-  15§        28.    38^  -^-  15f 

23.  7899  -j-  15f        26.    9894  ^  95f        29.    36J  -;-  17| 
Factor  and  cancel : 

30.  Divide  the  product  of  25  and  96  by  the  product  of 
15,  8,  and  12. 

31.  Divide  17280  by  1440. 

32.  What  is  the  quotient  of   21  x  28  X  36  divided  by 
27  X  14  X  6? 

33.  Divide  16  X  14  X  12  X  7  X  4  by  32  x  28. 


208  ARITHMETIC. 

Written  Review. 

1.  How  much  will  J  Ib.  of  coffee  cost  if  4  Ib.  cost  80/? 

2.  A   family   use   5  pt.   of    milk   daily.      How   many 
quarts  will  they  use  in  the  month  of  March  ? 

3.  How  much  will  2  dozen   bananas  cost  at  the  rate 
of  2  for  3  cents  ?     3  for  2  cents  ? 

4.  What  will  £  peck  of  apples  cost,  if  2  bushels  cost 
$1.50  ? 

5.  How  many  hours  in  the  month  of  February,  1896  ? 
1867? 

6.  If  I  buy  10  yd.  of  cloth  at  $2£  per  yard,  and  pay 
for  it  in  wool  at  $£  a  pound,  how  many  pounds  of  wool 
will  it  require  ?     (Use  cancellation.) 

7.  If  wood  is  worth  $4  a  cord  and  coal  $5  a  ton,  how 
many  cords  of  wood  will  pay  for  16  tons  of  coal  ?     (Use 
cancellation.) 

8.  What  will  be  the  cost  of  5  Ib.  6  oz.  of  steak  at  16/ 
a  pound  ? 

9.  My  lawn  is  120  ft.  long  and.  60  ft.  wide.      If  my 
lawn  mower  cuts  a  strip  16  inches  wide,  how  many  strips 
must  I  cut  to  mow  the  entire  lawn,  mowing  from  side  to 
side  ?    from  end  to  end  ?     (Diagram.)     How  many  miles 
do  I  walk  in  mowing  the  lawn  15  times  ? 

10.  40,000  is  what  part  of  half  a  million  ?     (Question.) 

11.  How  many  cubic  yards  of  air  in  a  schoolroom  36  ft. 
by  36  ft.  and  12  ft.  high  ? 

12.  If  there   are  45   children  in  the  room,   how  many 
cubic  yards  for  each  child  ? 

13.  How  much  do  I  gain  on  3  bushels  of  berries  bought 
at  $2  a  bushel  and  sold  at  11  /  a  quart  ? 

14.  How  many  sq.  inches  in  3  sq.  yards  ? 

15.  How  many  inches  in  3|  rods  ? 


FRACTIONS.  209 

Oral  Work. 

1.  If  a  pie  is  cut  into  8  equal  parts,  and  5  of  those  parts 
are  divided  among  10  boys,  what  part  of  the  pie  will  each 
boy  receive  ? 

2.  If  a  boy  can  ride  a  bicycle  18  miles  in  an  hour,  how 
far  can  he  ride  in  20  minutes  ? 

3.  If  I  can  buy  a  pound  of  raisins  for  ll/,  what  part  of 
a  pound  can  I  buy  for  8/  ? 

4.  If  coffee  is  37£/  a  pound,  how  many  pounds  can  be 
bought  for  $15  ? 

5.  When  coffee  is  37£/  a  pound,  what  will  40  pounds 
cost? 

6.  Tf  two  apples  are  divided  among  three  boys,  what 
part  of  an  apple  will  each  receive  ? 

7.  18  is  T3^  of  what  number  ? 

8.  If  3  boys  together  earn  5  dollars,  what  will  be  each 
boy's  portion  ? 

9.  How  much  is  £  of  five  ? 

10.  Which  is  greater  £  of  4  or  j  of  1  ? 

11.  How  much  is  $  of  5  ?  J  of  11  ?  f  of  6  ? 

12.  Among  how  many  boys  can  I  divide  5  oranges  giving 
each  boy  J  of  an  orange  ? 

13.  Reduce  to  whole  or  mixed  numbers,  ^  ;  -y- ;  -1/- ;  \6  ; 

V;  ¥;  ¥• 

14.  Reduce  to  improper  fractions,  7£ ;   14J ; 
5;  8;  8|. 

15.  Reduce  2J  to  8ths. 

16.  How  many  bushels  in  7  pecks  ? 

17.  How  many  feet  in  28  inches  ? 

18.  How  many  gallons  in  10  quarts  ? 

19.  What  part  of  a  gross  is  a  dozen  ? 


210  ARITHMETIC. 

Written  Work. 

1.  How  many  loads  of   earth  must  be  taken  from  a 
cellar  32  ft.  long,  27  ft.  wide,  and  7  ft.  deep  ? 

2.  Find  the  cost  of  14  cwt.  of  hay  at  $12  a  ton. 

3.  When  is  a  fraction  in  its  lowest  terms  ? 

4.  A  room  is  18 J-  ft.  long,  15  ft.  wide,  and  9£  ft.  high. 
How  many  square  yards  of  plaster  are  needed  for  the  walls 
and  ceiling  ? 

5.  Cover  the  floor  of  above  room  with  carpet  }  yards 
wide. 

6.  How  many  yards  of  lining  J  yd.  wide,  will  it  take 
to  line  a  quilt  2j  yd.  square  ? 

7.  A  silver  pitcher  weighs  3  Ib.  2  oz.     What  will  it 
cost  at  $.15  a  pwt. 

8.  How  many  gallons  of  water  in  a  cistern  8  X  5  X 
7  ft.  ? 

9.  Add:    9857,    7783,    8939,  2791,  9367,  4683,   8479, 
9847. 

10.  [(496  X  37)  -  6453]  -^  87  =  ? 

11.  Eeduce  f  of  T\  of  ££  of  fa  of  ft  of  }|  to  a  simple 
fraction. 

12.  What  is  a  prime  number  ? 

13.  What  is  a  composite  number  ? 

14.  What  is  the  difference  between  5f  +  8|  and  3^  + 
4f? 

15.  How  much  will  a  barrel  of  cider  cost  at  3 \fi  a  pint  ? 

16.  Bought  4765  laths  at  $1.98  per  M.     What  was  the 
cost? 

17.  Find  the  cost  of  3  gross  of  buttons  at  33  J/  a  doz. 

18.  Paid  $3.50  for  a  bushel  of  chestnuts.     What  must  I 
ask  per  quart  to  gain  $1.30  ? 


MEASUREMENTS.  211 

1.  How  many  cubic  feet  in  a  solid  block  measuring  2 
yards  on  each  edge  ? 

2.  An  acre  of  land  costs  $420.     How  much  will  a  square 
rod  cost  ? 

3.  In  j§  how  many  20ths  ? 

4.  What  is  the  value  of  38  Ib.  8  oz.  pure  gold  at  $1.04 
a  pennyweight  ? 

5.  How  many  yards  of  carpet  27  in.  wide  will  cover  a 
floor  12£  by  14  ft.  ? 

6.  How  many  cubes  3  X  4  x  2  in.  can  be  packed  into  a 
box  8  X  4  X  6  ft.  ? 

7.  10  sq.  rd.  are  what  part  of  an  acre  ? 

8.  A  room  40  ft.  square  contains  20000  cu.  ft.  of  air. 
How  high  is  it  ? 

9.  From  f  of  4J  take  £  of  3|. 

10.  How  many  days  in  the  first  5  months  of  a  leap  year  ? 

11.  What  are  the  dimensions  of  a  5  ft.  cube  in  inches  ? 

12.  When  f  of  a  year  has  passed,  how  many  days  remain  ? 

13.  Are  all  the  factors  of  24  found  in  56  ? 

14.  Find  the  factors  of  108. 
7201   x  207    =  ? 

144 

16.  Find  the  cubic  inches  in  a  3J  ft.  cube  ? 

17.  The  capacity  of  a  room  12  ft.  square  is  1368  cubic 
feet.     What  is  its  height  ? 

18.  How  many  gallons  of  water  will  a  cistern  11  X  7  X  6 
ft.  hold  ?     (Cancel.) 

19.  How  many  inches  in  all  the  edges  of  a  2  ft.  cube  ? 

20.  How  many  gallons  in  a  tank,  4  ft.  6  in.  long,  2  ft. 
8  in.  wide,  and  1  ft.  6  in.  deep  ? 


212  ARITHMETIC. 

1.  Find  the  area  of  one  face  of  a  cube  2  ft.  9  in.  long. 

2.  What  is  meant  by  debtor  ?     Creditor  ? 

3.  Make  the   following  into  a  bill   and   receipt   it,  — 
2£  Ib.  sugar  at  5/ ;  9  Ib.  beef  at  8/ ;  2  Ib.  coffee  at  37£/ ; 
1  Ib.  tea  at  50/ ;  2  J  Ib.  cheese  at  13/. 

4.  What  are  the  prime  factors  of  36  ? 

5.  What  are  the  factors  of  any  product  ? 

6.  How  much  hay  at  $16  a  ton  will  $4  buy  ? 

7.  How  many  feet  of  fence  will  enclose  a  lot  80  rd. 
square  ? 

8.  £  of  a  hogshead  of  vinegar  leaked  away.     How  many 
quarts  remained  ? 

9.  If  a  bushel  of  chestnuts  is  bought  for  $4  and  sold 
at  12/  a  quart,  what  is  the  loss  ? 

10.  5280  ft.  =  ?  366  da.  =  ? 
2240  Ib.  =  ?  49  Ib.  =  ? 

128  cu.  ft.  =  ?  29  da.  =  ? 

11.  (j  of  6i)  -  (i  of  3|)  =  ? 

12.  If    I   use  14  from  a  great  gross  of  buttons,  how 
many  buttons  will  be  left  ? 

13.  A  room  is  40  ft.  square  and  12  ft.  high.     How  many 
sq.  yards  of  plastering  in  the  walls  and  ceiling,  making  no 
allowance  for  openings  ? 

14.  What  would  it  cost  to  carpet  the  above  room  with 
carpet  1  yd.  wide  at  $1 J  a  yard  ? 

15.  I  use  3J  cu.  feet  of  ice  a  day.     How  many  cubic  feet 
Will  I  use  during  the  spring  and  summer  months  ? 

16.  If  4  tons  of  coal  cost  $17,  what  will  3  cwt.  cost  ? 

17.  How  many  cubic  inches  in  a  cubic  block  whose  edge 
measures  four  feet  ? 

18.  Change  3J|  to  200ths. 


DECIMALS.  213 

DECIMAL  FRACTIONS. 

A  Common  Fraction  is  generally  expressed  by  placing 
the  denominator  below  the  numerator. 

A  Decimal  Fraction  has  a  denominator,  but  the  latter 
is  not  generally  written. 

The  denominator  of  a  common  fraction  may  be  any 
number. 

The  denominator  of  a  decimal  fraction  must  be  10,  or  100, 
or  1000,  etc. 

NOTE.  —  The  word  decimal  comes  from  the  Latin  word 
decem,  ten,  and  so  the  denominator  of  every  decimal  frac- 
tion is  10,  or  10  X  10,  or  10  X  10  X  10,  etc. 

A  Decimal  Fraction,  or  Decimal,  is  a  fraction  whose  unit 
is  divided  into  tenths,  hundredths,  thousandths,  etc. 

A  Decimal  is  always  written  at  the  right  of  a  period  (.), 
called  the  Decimal  Point. 

We  use  the  decimal  point  in  writing  U.S.  money  to 
separate  the  dollars  from  the  cents  and  mills.  5  dollars 
and  28  cents  is  written  $5.28.  But  28  cents  is  ffo  of  a 
dollar;  hundredths  therefore  are  written  like  cents,  with 
two  decimal  figures. 

NOTE.  —  Any  figure  at  the  right  of  the  decimal  point  is 
a  decimal  figure. 

Tenths  are  written  like  dimes,  with  one  decimal  figure. 

fV  =  -3  ;  T8u  =  -8  5  yV  =  -7- 

Hundredths    are    written    with    two    decimal    figures, 

^  =  •28;  flfr  =  .39;  T{fo  =  .06. 

Thousandths   are   written   with   three    decimal   figures, 

=  -025. 


Name  the  denominators  : 

1.  .6  3.    .105  5.    .05 

2.  .17  4.    .006  6.    .225 


214  ARITHMETIC. 

Change  to  decimal  form  : 

1  vU*  6       •*  ^Ar  11        •?••&  16 

2  *U*  7      -vU*  12       i  i  17 
o      .J'jiJL             Q     --A»-                   1^-2-                    18 

4.  _6_  Q  6  14.500  1Q 

*•    TO  *'    1015  "•    TOOO  i^< 

5.  y\^  10.         y-J-g-g  15.         y^  20. 

Change  to  common  fractions,  and  read  : 

21.  .36  26.    .485  31.  5.6 

22.  .7  27.    .016  32.  5.06 

23.  .125  28.    .16  33.  5.006 

24.  12.2  29.    .06  34.  5.600 

25.  6.25  30.    .6  35.  5.060 
Write,  first  as  common  fractions,  then  as  decimals : 

36.  Six  tenths. 

37.  Seventy-five  hundredths. 

38.  One  hundred  twenty-five  thousandths. 

39.  Sixteen,  and  forty-eight  hundredths. 

40.  Twelve,  and  four  tenths. 

41.  Six  tenths. 

42.  Six  hundredths. 

43.  Six  thousandths. 

44.  How  many  decimal  figures  are  required  to  express 
thousandths  ?  hundredths  ?  tenths  ? 

45.  Read  the  numerators  only  in  Examples  36  to  43. 
Write  the  following  as  decimals,  and  read  the  numerator 

of  each,  then  the  denominator  of  each. 

46.  Two  hundred  eighty-two  thousandths. 

47.  Fifty-six  hundredths. 

48.  Seven  tenths. 

49.  Six  hundred  thousandths. 


DECIMALS.  215 

Oral  Work. 

1.  What  part  of  10  units  is  1  unit  ? 

2.  What  part  of  1  ten  is  1  unit  ? 

3.  What  part  of  2  hundreds  is  2  tens  ? 

4.  In  the  number  555,  what  is  the  value  of  the  first 
5  at  the  right  ?  the  second  5  ?  the  third  5  ? 

5.  Upon  what  does  the  value  of  any  figure  depend  ? 

6.  The  value  of  the  first  five  is  what  part  of  the  value 
of  the  second  five  ?     (Question.) 

7.  -fa  is  what  part  of  2  units  ? 

8.  In  the  number  5.5  the  value  of  the  right-hand  5  is 
what  part  of  the  value  of  the  left-hand  5  ?     (Question.) 

9.  Write  five  and  five-tenths  decimally. 

10.  .5  is  what  part  of  5  ? 

11.  In  the  decimal  .555  what  is  the  value  of  the  first  5 
to  the  right  ?  the  second  5  ?  the  third  5  ? 

12.  How  much  greater  is  the  value  of  the  third  5  than 
the  second  5  ?     (Question.) 

13.  How  much  greater  is  the  second  5  than  the  first  5  ? 
In  the  number  555.555  we  have  found  that  the  value  of 

each  5  is  ^  as  much  as  the  next  5  to  the  left.  Also  that 
the  value  of  any  5  is  10  times  as  great  as  the  value  of  the 
next  5  to  the  right. 

In  decimals  as  in  integers,  any  figure  removed  one  place 
to  the  right  is  diminished  tenfold,  and  when  removed  one 
place  to  the  left  it  is  increased  tenfold. 

14.  In  the  number  32.6  what  would  be  the  value  of  the 
2  if  it  were  removed  one  place  to  the  right  ?     One  place  to 
the  left  ? 

Read: 

15.  .222  17.    22.2 

16.  2.22  18.   222. 


216  ARITHMETIC. 

Integers  and  Decimals. 


I  ii      !l 

•i  1 1      fl  *  i       i  i  I 

l!j   lis     HI    HI 

^         WHH         WHO  HKH          H  W  S 

4,        243,       684       .268,         504 

The  number  is  read  4  million,  243  thousand,  684  and 
268  thousand  504  millionths. 

To  read  decimals  : 

For  the  numerator,  read  the  decimal  as  an  integer. 

For  the  denominator,  give  the  denomination  of  the  last 
figure. 

NOTE.  —  The  denominator  of  a  decimal  is  always  named, 
but  seldom  written. 

In  reading  an  integer  and  a  decimal,  read  "  and  "  where 
the  decimal  point  occurs. 

What  is  the  denominator  when  the  decimal  has  one  fig- 
ure ?  two  figures  ?  three  figures  ?  four  figures  ?  five  figures  ? 
six  figures  ?  seven  figures  ? 

Eead: 

1.  .368  7.    28.3005  13.    .4983695 

2.  .894  8.    .28962  14.    4.98369 

3.  .5328  9.    15.60534  15.    49.8369 

4.  .2053  10.   37.00537  16.   498.369 

5.  25.623  11.    25.203602  17.    .000400 

6.  7.0063  12.    38.000006  18.    .0004 

19.  In  Example  11  remove  the  point  two  places  to  the 
right  and  read.     Four  places  to  the  right.     One  place  to 
the  left. 

20.  Kead  denominators  only,  in  the  last  five  Examples. 


DECIMALS.  217 

To  write  a  decimal : 

Write  the  numerator ;  prefix  naughts  when  necessary  to 
express  the  denominator ;  place  the  point  at  the  left. 

How  many  decimal  figures  are  required  to  express  tenths  ? 
hundredths  ?  thousandths  ?  ten-thousandths  ?  hundred- 
thousandths  ?  millionths  ?  ten-millionths  ? 

Write  decimally : 

1.  Eight  tenths. 

2.  29  hundredths. 

3.  Sixteen,  and  284  thousandths. 

4.  4584  ten-thousandths. 

5.  Twenty-five  hundredths. 

6.  Twenty-five  thousandths. 

7.  Twenty-five  .ten-thousandths. 

8.  Twenty-five  hundred-thousandths. 

9.  Twenty-five  millionths. 

10.  1650,  and  464  thousandths. 

11.  One  thousand  one,  and  36  hundred-thousandths. 

12.  Sixteen,  and  six  thousandths. 

13.  Seven  hundred  eighty-four  millionths 

14.  Twelve  hundred-thousandths. 

15.  Seventy-five  ten-thousandths. 

16.  Seven  hundred  fifty  ten-thousandths. 

17.  Seven  thousand  five  hundred  ten-thousandths. 

18.  324  millionths. 

19.  7685  hundred-thousandths. 

20.  One  million  three  hundred  six  thousand  four  hundred 
two,  and  three  hundred  five  thousand  four  hundred  ten 
ten-millionths. 

21.  Three  hundred-thousandths. 


218  ARITHMETIC. 

Oral  Work. 

1.  In  the  three  decimals,  .4,  .40,  .400,  is  there  any  differ- 
ence in  value  ? 

2.  What  is  the  effect  when  a  naught  is  annexed  to  a 
decimal  ? 

3.  What  is  the  effect  when  a  naught  is  annexed  to  an 
integer  ?     Give  an  example. 

4.  In  the  decimals,  .4,  .04,  .004,  is  there  any  difference 
in  value? 

5.  What  is  the  effect  when  a  naught  is  prefixed  to  a 
decimal  ?  two  naughts  ?     Give  examples. 

6.  What  is  the  effect  when  a  naught  is  prefixed  to  an 
integer  ? 

Naughts  annexed  to  decimals  do  not  change  their  values. 
(Prove  this.) 

For  each  naught  prefixed  to  a  decimal  the  value  is  dimin- 
ished tenfold.  (Prove.) 

The  denominator  of  a  decimal  when  expressed  is  always 
1  with  as  many  naughts  as  there  are  figures  in  the  numera- 
tor. (Prove.) 

REDUCTION   OF  DECIMALS. 

Decimals  may  be  reduced  to  a  common  denominator  by 
annexing  naughts  sufficient  to  give  the  same  number  of 
decimal  figures  to  all  the  decimals. 

Eeduce  to  a  common  denominator : 

7.  .5,  .365,  and  .4689. 

8.  .18963,  .5,  7.84,  .16005. 

9.  .28,  3.5,  .00005,  .256. 

10.  .5,  .05,  .005,  .0005,  .00005. 

11.  .0463,  .03,  .1,  .100010. 

12.  .38,  1.16,  .4,  78.592. 


DECIMALS.  219 

To  reduce  a  decimal  to  a  common  fraction. 

1.    Eeduce  .375  to  a  common  fraction. 

SOLUTION.  —  .375  as  a  common  fraction  is  --5   -375  = 


Rule.  —  Write  the  numerator,  omitting  the   point,  sup- 
ply the  denominator,  and  reduce  to  lowest  terms. 
Eeduce  to  common  fractions  : 

2.  .25  8.    .125  14.    .368 

3.  .35  9.    .875  15.   16.75 

4.  .75  10.    .375  16.    .00125 

5.  .64  11.    .455  17.    .054 

6.  .52  12.   .025  18.    .0250 

7.  .38  13.    .561  19.    .01375 
20.   Eeduce  .37^  to  a  common  fraction. 

SOLUTION.  -  .37*  =  ^  =         =         = 

Eeduce  to  common  fractions  : 

21.  .12£  24. 

22.  .62J  25.    .03|  28.    .66§ 

23.  .06£  26.    .25|  29.    .36J 
Eeduce  to  mixed  numbers  : 

30.    16.25;  2.33  J  ;  34.75. 

To  reduce  a  common  fraction  to  a  decimal. 

Eeduce  J  to  a  decimal. 

J  =  3  times  £.     3  =  (3.0)  30  tenths. 

£  of  3.0  =  (.7)  7  tenths  and  2  tenths  remainder. 

2  tenths  =  20  hundredths.     £  of  .20  =  .05. 

Hence  J  =  .7  +  .05  =  .75. 

Rule.  —  Annex  decimal  naughts  to  the  numerator,  and 
divide  by  the  denominator.  Point  off  in  the  quotient  as 
many  decimal  places  as  there  are  naughts  annexed. 


220  ARITHMETIC. 

The  division  will  not  always  be  exact.  In  such  cases, 
write  the  remainder  over  the  divisor  as  a  common  fraction, 
or  place  the  sign  (+)  after  the  decimal  to  show  that  the 
result  is  incomplete. 

Thus,  |  =  .142f,  or  .142  +. 

Reduce  to  decimals  : 


1-  I 

6-    i 

n-  i* 

16.    § 

2.    | 

7-    } 

12.    /s 

17-    ft 

3-    $ 

8.    § 

13.    J 

18.    /5 

4.    J 

9-    A 

14.    {2 

w-  i* 

6-    ft 

io-  51 

15.    3A 

20.    2^ 

Add  :  .35,  4.375,  28.3065. 

.35  RULE.  —  Write  the  numbers  so  that  the  deci- 

4.375       mal  points  stand  in  a  column.     Add  as  in  inte- 
28.3065     gers,  and  place  the  point  in  the  sum  directly 
under  the  points  above. 

Add: 

2.   3.25  3.  4.5  4.   .004 
7.163          .168         4.1 
15.0032        2.12         16.1563 

5.  .175  +  1.75  +  17.5  +  175. 

6.  145  +  14.5  +  1.45  +  .145  +  .0145. 

7.  3.2  +  14.0063  +  .006  +  25,384  +  .1. 

8.  .8  +  .446  +  59.3  +  2.575  +  1.0056  +  .3. 

9.  1.45  +  2.365  +  96  +  .96  +  15.863  +  4.3  +  .0004. 

10.  446  +  44.6  +  37562  +  9  +  .8  +  .321  +  .16. 

11.  21.0005  +  .3842  +  .1  +  .005  +  3.6  +  .158. 

12.  1.0006  +  2001.1  +  .003  +  5.5  +  11.1111. 


DECIMALS.  221 

SUBTRACTION. 

Rule.  —  Write  the  numbers  so  that  the  decimal  point  of 
the  subtrahend  stands  directly  under  the  decimal  point 
of  the  minuend,  subtract  as  in  integers,  and  place  the  point 
directly  under  the  points  above. 

NOTE.  —  It  is  sometimes  convenient  to  give  the  decimals 
the  same  denominator,  by  annexing  decimal  naughts. 
Subtract : 

1.   24.3  2.    2.86  3.   4.  4.    2.46 

4.5  1.325  1.15  .005 

Find  remainders  : 

5.  7  -  .15  10.  29.325  -  15.14 

6.  1  -  .004  11.  3.852  -  .125 

7.  13  -  2.1  12.  1.1111  -  .0011 

8.  3.256  -  1.05  13.  500  -  .05 

9.  256.1  -  1.256  14.  25.3894  -  15.005 

15.  From  twenty-eight,  and  twenty-five  thousandths  take 
fourteen,  and  twenty-five  hundredths. 

16.  From  one  tenth  take  one  thousandth. 

17.  Which    is    the    greater,   fifty   thousandths    or    five 
hundredths  ? 

18.  Take  one  thousandth  from  one  thousand. 

19.  From  5  hundred  take  5  hundredths. 

MUL  TIPLICA  TION. 
Oral  Work. 

How  much  is  2  times  .3  ?   3  times  .3  ?  4  times  .3  ? 
7  times  .02  =  ?  12  times  .06  =  ?  12  times  $.12  =? 

AXA  =  T**5  .1  X.I  =  .01. 

-3  X  .05  =  .015. 
.3X.3=.09. 


222  ARITHMETIC. 

T^  x  T3ff  =  rMff  How  many  naughts  in  the  denom- 
inator of  the  product  ? 

How  many  naughts  in  the  denominators  of  both  factors  ? 

Every  decimal  has  a  corresponding  common  fraction,  and 
for  each  naught  in  the  denominator  of  the  common  frac- 
tion, there  is  a  decimal  figure  in  the  decimal. 

.05  X  .3  =  .015  How  many  decimal  figures  in  both 
factors  ? 

Rule.  —  Multiply  as  in  integers,  and  point  off  from  the 
right  of  the  product  as  many  decimal  figures  as  there  are 
decimal  figures  in  both  factors. 

NOTE.  —  If  there  are  not  figures  enough,  prefix  naughts. 

Naughts  at  the  right  of  a  decimal  have  no  value,  and 
may  be  omitted. 

2.8  1.25  .005  25 

X  8  .6  .03  .06 

22.4  .750  .00015  1.50 

Find  the  products : 

1.  .18  X  .15  8.  13.3  X  1.3 

2.  1.0005  X  .2  9.  100  X  .01 

3.  2.5  X  .06  10.  100.56  X  .0005 

4.  56  X  .005  11.  25.32  x  1.05 

5.  .005  X  1.6  12.  2.84  x  2£ 

6.  25.05  X  1.15  13.  3.28  X  12J 

7.  2.863  X  100  14.  1.111  X  1000 
To  multiply  by  10,  100,  1000,  etc. 

1.265  1.  Multiply  1.265  by  100. 

100          Remove  the  point  one  place  to  the  right  for 
126.500     every  naught  in  the  multiplier. 
Do  not  write  the  multiplier. 


DECIMALS.  223 

Oral  Work. 

Multiply : 

2.  3.84  by  10  7.  .3  by  100 

3.  12.63  by  100  8.  1.869  by  100 

4.  1.5555  by  1000  9.  32.856  by  1000 

5.  1.358  by  1Q  10.  138.56  by  1000 

6.  .25  by  1000  11.  11.11  by  100 

DIVISION. 

Since  in  multiplication  there  are  as  many  decimals  fig- 
ures in  the  product  as  in  both  factors,  in  division  the 
quotient  will  have  as  many  decimal  figures  as  the  number 
of  decimal  figures  in  the  dividend  exceeds  those  in  the 
divisor. 

.5)  12.685  Since  there  are  three  decimal  figures  in  the 
25.37  dividend  and  one  in  the  divisor,  there  must  be 
two  in  the  quotient.  Prove  by  multiplying  dividend  by 
quotient. 

In  all  cases  divide  as  in  integers,  then  place  the  decimal 
point. 

Divide  399.552  by  192. 

2.081 

192)  399.552  When  the  divisor  is  an  integer,  place  the 
point  in  the  quotient  directly  over  the  point 
in  the  dividend,  in  long  division  (directly 

1£^        under  in  short  division). 

192 

Prove  by  multiplying  the  divisor  by  the 

quotient. 

4)  12         If  we  multiply  both  dividend  and  divisor  by 
3      the  same  number,  the  quotient  will  not  be  changed. 
Multiply  both  4  and  12   by  2;   by  6;   by  any  number. 
What  is  the  effect  in  each  case  ? 
Divide  28.78884  by  1.25. 


224  ARITHMETIC. 

23.031  +         When  the  divisor  contains   decimal 
1.25')28.78  884         figures,  move  the  point  in  both  divisor 
and  dividend  as   many  places   to   the 
right  as  there  are  decimal  figures  in 
the  divisor,  then  place  the  point  in  the 
quotient    as    if    the    divisor   were    an 
~jcj4  integer. 

125  NOTE   1.  —  The   new  point  in   both 

9  dividend  and  divisor  may  be  placed  on 

a  line  with  the  tops  of  the  figures,  and  the  original  point 
may  stand,  to  preserve  the  reading  of  the  decimals. 

NOTE  2.  —  In  the  above  example,  the  moving  of  the 
point  two  places  to  the  right  in  both  dividend  and  divisor 
is  equivalent  to  multiplying  each  by  100. 

NOTE  3.  —  If  the  quotient  does  not  have  a  sufficient 
number  of  figures,  prefix  naughts. 

NOTE  4.  —  Before  commencing  to  divide  see  that  there 
are  at  least  as  many  decimal  places  in  the  dividend  as  in 
the  divisor. 

NOTE  5.  —  If  there  is  a  remainder,  after  all  the  figures 
of  the  dividend  are  used,  annex  decimal  naughts  and  con- 
tinue the  division. 

NOTE  6.  —  It  is  not  usually  necessary  to  have  more  than 
four  decimal  figures  in  the  quotient. 
Divide  .125  by  .5 
Divide  1.25  by  .5 
Divide  12.5  by  .5 

Divide  at  sight : 

1.   3)3.33  4.    .03).333  7.    .5)25 

5.  .003).333  8.    .05).25 

6.  5^)2.5  .07).28 


DECIMALS. 


225 


18.  376  - 

19.  376  - 

20.  37.6 

21.  3.76 


.6 
.06 
.6 

-  .06 


22.  1.875  -f-  .005 

23.  15.55  ^  .1 

24.  1  +  .1 

25.  .1  -T-  1 


Find  quotients,  and  prove  : 

10.  3.57  -T-  .7 

11.  .488  -*-  .12 

12.  16.55  -4-  .05 

13.  13.13  -^  1.3 

14.  1.111  --  .01 

15.  5555  ^-  .5 

16.  .875  -f-  .05 

17.  73.5  ~  1.05 

Divide : 

26.  Twenty-five  ten-thousandths  by  25  hundredths. 

27.  4678  hundred-thousandths  by  9  ten-thousandths. 

28.  3582  ten-thousandths  by  3  hundredths. 

To  divide  by  10,  100,  1000,  etc.,  remove   the   decimal 
point  one  place  to  the  left  for  each  naught  in  the  divisor. 

Divide  at  sight : 

33.  100)189.36 

34.  100).189 

35.  100)148.369 


29.  10)365.8 

30.  10}5_ 

31.  10)148.963 

32.  10)115.55 


Eead  and  add  : 


1. 


32.065 
6.006 
4.25 
.032 
.25 
25.01 
111.11 


2. 


36.9486 
2583.04 

4.9602 

15.15 

100.001 

56.56 

141.141 


226  ARITHMETIC. 

Review  of  Decimals. 

1.  Tell  where  to  place  the  decimal  point  in  any  product. 

2.  In  any  quotient. 

3.  In  any  remainder. 

4.  In  any  sum. 

5.  From  1  take  1  millionth. 

6.  Add  1  tenth,  1  hundredth,  and  1  thousandth. 

7.  Find  the  product  of  1  multiplied  by  .15. 

8.  Multiply  at  sight :  36.984  by  1000. 

9.  Divide  at  sight :  159.83  by  1000. 
Change  to  decimals : 

10.  i,  f,  *,  16},  255. 
Change  to  common  fractions  : 

11.  .28,  .38,  .375,  15.125. 

12.  If  John  earns  $8  in  a  week,  how  much  can  he  earn 
in  7.5  weeks  ? 

13.  If  a  barrel  of  flour  costs  $5.25,  how  many  barrels  can 
be  bought  for  $105  ? 

14.  How  many  rods  of  fence  around  a  rectangular  field 
10.018  rd.  long,  and  6.2892  rd.  wide  ? 

15.  Eeduce  5.75  rods  to  feet. 

16.  How  many  rods  in  247.5  feet  ? 

. 

17.  What  is  the  effect  when  a  decimal  figure  is  removed 

one  place  to  the  left  ?  to  the  right  ? 

18.  What  is  the  effect  when  an  integral  figure  is  removed 
one  place  to  the  left  ?     One  place  to  the  right  ? 

19.  At  15^  a  peck,  how  many  pecks  of  pop-corn  can  be 
bought  for  $3.75  ? 

20.  What  is  the  cost  of  28.78  yd.  of  cloth  at  $3.15  a 
yard? 


DECIMALS.  227 

Written  Work. —  Short  Methods. 
1.    Multiply  2.222  by  200. 

Remove  the  point  two  places  to  the  right,  and  multiply 
by  2  ;  thus : 

222.2  X  2  =  444.4.    Am. 

Multiply  and  prove  : 

2.  6.84  X  500  5.   3.553  X  800 

3.  28.96  X  2000  6.   4.583  X  4000 

4.  1.876  X  80  7.    156.2  X  200 
8.    Divide  444.4  by  200. 

Eemove  the  point  two  places  to  the  left,  and  divide  by 
2;  thus: 

4.444  _=_  2  =  2.222.    Ans. 

Divide  and  prove : 

9.  369.5  -f-  500  15.  2.835  -=-  700 

10.  36.66  -f-  60  16.  35.46  -f-  40 

11.  36.48  -4-  8000  17.  808  -r-  700 

12.  .159  -r-  900  18.  2585  -r-  5000 

13.  172.8  -f-  120  19.  3.672  -f-  6000 

14.  1.44  +  1200  20.  25.55  -5-  50 

21.  How  much  is  j  of  324  ? 

22.  How  much  is  .75  of  324  ? 
Oral  Work.  —  Questions  of  Relation. 

23.  .5  of  16  equals  what  ? 

24.  8  is  what  decimal  part  of  16  ? 

25.  8  is  .5  of  what  ? 

26.  How  much  is  .06  of  $200  ? 

27.  $12  is  what  decimal  part  of  $200  ? 

28.  Five  cents  is  what  part  of  $5  ?     Express  the  answer 
as  a  decimal  fraction. 


228  ARITHMETIC. 

MISCELLANEOUS  REVIEW. 

1.  How  much  must  be  paid  for  lathing  and  plastering 
the  walls  and  ceiling  of  a  room  36  ft.  long  and  20  ft.  wide 
at  25  ct.  a  square  yard  ? 

2.  How  many  cubic  yards  of  earth  were   removed  in 
digging  an  excavation  for  a  cellar  28  ft.  9  in.  long,  18  ft. 
8  in.  wide,  and  5  ft.  6  in.  deep  ? 

3.  How  many  yards  of  carpet  27  inches  wide  will  cover 
a  room  22  ft.  6  in.  long,  and  18  ft.  wide. 

4.  How  deep  is  a  lot  100  ft.  wide  that  contains  20450 
sq.  ft.  ? 

5.  How  many  square  inches  in  the  surface  of  a  12-inch 
cube? 

6.  In  a  pile  of  wood  64  ft.  long,  24  ft.  wide,  and  8  ft. 
high,  how  many  cords  ? 

7.  A  block  of  marble  is  3  ft.  long,  20  in.  wide,  and  18 
in.  thick.     How  many  3-inch  cubes  can  be  cut  from  it  ? 
(Solve  by  calculation.) 

8.  A  man  purchased  4  pieces  of  sheeting,  each  contain- 
ing 35  yd.,  at  10  cents  a  yard,  and  pays  for  it  in  eggs  at 
15  cents  a  dozen.     How  many  dozen  eggs  does  it  require  ? 

9.  Divide  the  product  of  8,  7,  5,  3,  6  by  the  product  of 
15,  4,  7. 

10.  What  is  a  Eectangle  ? 

11.  Define  a  Proper  Fraction. 

12.  Which  is  greater,  and  how  much,  |  of  24,  or  £  of  30  ? 

13.  If  tea  is  worth  $£  a  pound,  how  much  can  be  bought 
for  $J  ?     (Question.) 

14.  What  is  the  cost  of  40.5  tons  of  coal  when  .3  of  a 
ton  costs  $4.48  ? 

15.  John  had  48  marbles  and  lost  .25  of  them.     How 
many  did  he  lose  ? 


REVIEW.  229 

1.  If  f  of  an  acre  of  land  produces  20  bushels  of  grain, 
how  many  bushels  will  4  acres  produce  ? 

2.  How  many  yards  of  cloth  at  $3.75  a  yard  can  be 
purchased  for  $288.75? 

3.  869.44  X  2000  =  ? 

4.  869.44  -r-  2000  =  ? 

5.  How  many  dozen  eggs  at  12  cents  a  dozen  will  pay 
for  96  bushels  of  corn  at  60  cents  a  bushel  ? 

6.  A  coal-dealer  received  12  car-loads  of   coal.     Each 
car  contained  18000    pounds.      How   many  tons   did   he 
receive  ? 

7.  What  is  the  cost  of  3142  pounds  of  plaster  at  $3.75 
a  ton? 

8.  If  a  man's  income  is  $1800  a  year,  and  his  expenses 
are  $4.50  a  day,  how  much  can  he  save  in  a  year  ? 

9.  In  how  many  years  will  a  man  lay  up  $1000  if  he 
earns  $75  a  month,  and  his  expenses  amount  to  $35  a 
month  ? 

10.  A  boy  sells  oranges  at  the  rate  of  12  for  36  cents. 
How  much  does  he  receive  for  48  oranges  ?  for  53  oranges  ? 
for  38  oranges  ? 

11.  The  divisor  is  3.875  and  the  quotient  46.5,  what  is 
the  dividend  ? 

12.  The  quotient  is  206.48  and  the  dividend  268.432, 
what  is  the  divisor? 

13.  How  many  16ths  in  |  ? 

14.  When  it  costs  $1.50  to  travel  75  miles  on  the  railroad, 
how  much  will  it  cost  to  travel  375  miles  ? 

15.  $12  is  .06  of  how  many  dollars  ? 

16.  What  decimal  part  of  a  bushel  is  a  peck  ? 

17.  What  part  of  a  yard  is  1.5  feet  ? 


230  ARITHMETIC. 

1.  Find  the  product  of  248  and  763. 

2.  Find  a  quotient,  using  6954  and  218.     Find  another. 

3.  The  sum  of  four  numbers  is  12006 ;  6492,  3005,  and 
943  are  three  of  the  numbers.     Find  the  other. 

4.  A  field  213  rd.  long  and  180  rd.  wide  contains  how 
many  sq.  rd.  ?     How  many  acres  ? 

5.  Multiply  f  of  432  by  $\. 

«•    i  +  A-s-*  =  ?     (*  + A)  •*»  =  ? 

7.  What  is  a  numerator  ?     What  is  a  fraction  ? 

8.  Find  the  area  of  the  floor  in  a  room  15  ft.  long  and 
12  ft.  wide. 

9.  Write  three  factors  of  72. 

10.  Find  the  value  of     15  X  75  x  81 

6  X  9  X  3  X  25 

11.  How  many  cubic  inches  in  a  marble  block  6  ft.  long, 
4  ft.  wide,  and  2  ft.  9  in.  thick  ? 

12.  If  6  cwt.  of  coal  cost  $1.80,  what  will  a  ton  cost  ? 

13.  How  many  boards  12  ft.  long,  and  6  inches  wide,  will 
make  a  floor  24  X  18  ft.  ?     (Cancel.) 

14.  A  pile  of  wood  4  ft.  long,  4  ft.  wide,  and  4  ft.  high, 
will  cost  how  much,  at  $6.25  a  cord  ? 

15.  429  has  three  factors.     If  11  is  one  of  them,  what 
are  the  other  two  ? 

16.  A  field  is  30.65  rd.  wide,  and  nine  times  as  long  as  it 
is  wide.     Find  its  area  in  sq.  rd. 

17.  How  many  thousandths  in  2  ? 

18.  2.0705  -T-  2.05  =  ?     Write  your  answer  in  words. 

19.  Write  a  bill  of  the  following  sale  to  James  P.  Brown  : 
12J  tons  of  coal  at  $6.25;  18  bushels  of  corn  at  $.75; 
478  ft.  of  lumber  at  $17 


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